Calculus Examples

$y^{2} - 3 x y + x^{2} = 7$

Step 1

Differentiate both sides of the equation.

$\frac{d}{d x} (y^{2} - 3 x y + x^{2}) = \frac{d}{d x} (7)$

Step 2

Differentiate the left side of the equation.

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Step 2.1

By the Sum Rule, the derivative of $y^{2} - 3 x y + x^{2}$ with respect to $x$ is $\frac{d}{d x} [y^{2}] + \frac{d}{d x} [- 3 x y] + \frac{d}{d x} [x^{2}]$ .

$\frac{d}{d x} [y^{2}] + \frac{d}{d x} [- 3 x y] + \frac{d}{d x} [x^{2}]$

Step 2.2

Evaluate $\frac{d}{d x} [y^{2}]$ .

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Step 2.2.1

Differentiate using the chain rule, which states that $\frac{d}{d x} [f (g (x))]$ is $f' (g (x)) g' (x)$ where $f (x) = x^{2}$ and $g (x) = y$ .

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Step 2.2.1.1

To apply the Chain Rule, set $u$ as $y$ .

$\frac{d}{d u} [u^{2}] \frac{d}{d x} [y] + \frac{d}{d x} [- 3 x y] + \frac{d}{d x} [x^{2}]$

Step 2.2.1.2

Differentiate using the Power Rule which states that $\frac{d}{d u} [u^{n}]$ is $n u^{n - 1}$ where $n = 2$ .

$2 u \frac{d}{d x} [y] + \frac{d}{d x} [- 3 x y] + \frac{d}{d x} [x^{2}]$

Step 2.2.1.3

Replace all occurrences of $u$ with $y$ .

$2 y \frac{d}{d x} [y] + \frac{d}{d x} [- 3 x y] + \frac{d}{d x} [x^{2}]$

Step 2.2.2

Rewrite $\frac{d}{d x} [y]$ as $y'$ .

$2 y y' + \frac{d}{d x} [- 3 x y] + \frac{d}{d x} [x^{2}]$

Step 2.3

Evaluate $\frac{d}{d x} [- 3 x y]$ .

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Step 2.3.1

Since $- 3$ is constant with respect to $x$ , the derivative of $- 3 x y$ with respect to $x$ is $- 3 \frac{d}{d x} [x y]$ .

$2 y y' - 3 \frac{d}{d x} [x y] + \frac{d}{d x} [x^{2}]$

Step 2.3.2

Differentiate using the Product Rule which states that $\frac{d}{d x} [f (x) g (x)]$ is $f (x) \frac{d}{d x} [g (x)] + g (x) \frac{d}{d x} [f (x)]$ where $f (x) = x$ and $g (x) = y$ .

$2 y y' - 3 (x \frac{d}{d x} [y] + y \frac{d}{d x} [x]) + \frac{d}{d x} [x^{2}]$

Step 2.3.3

Rewrite $\frac{d}{d x} [y]$ as $y'$ .

$2 y y' - 3 (x y' + y \frac{d}{d x} [x]) + \frac{d}{d x} [x^{2}]$

Step 2.3.4

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 1$ .

$2 y y' - 3 (x y' + y \cdot 1) + \frac{d}{d x} [x^{2}]$

Step 2.3.5

Multiply $y$ by $1$ .

$2 y y' - 3 (x y' + y) + \frac{d}{d x} [x^{2}]$

Step 2.4

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 2$ .

$2 y y' - 3 (x y' + y) + 2 x$

Step 2.5

Simplify.

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Step 2.5.1

Apply the distributive property.

$2 y y' - 3 (x y') - 3 y + 2 x$

Step 2.5.2

Remove unnecessary parentheses.

$2 y y' - 3 x y' - 3 y + 2 x$

Step 2.5.3

Reorder terms.

$2 y y' - 3 x y' + 2 x - 3 y$

Step 3

Since $7$ is constant with respect to $x$ , the derivative of $7$ with respect to $x$ is $0$ .

$0$

Step 4

Reform the equation by setting the left side equal to the right side.

$2 y y' - 3 x y' + 2 x - 3 y = 0$

Step 5

Solve for $y'$ .

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Step 5.1

Move all terms not containing $y'$ to the right side of the equation.

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Step 5.1.1

Subtract $2 x$ from both sides of the equation.

$2 y y' - 3 x y' - 3 y = - 2 x$

Step 5.1.2

Add $3 y$ to both sides of the equation.

$2 y y' - 3 x y' = - 2 x + 3 y$

Step 5.2

Factor $y'$ out of $2 y y' - 3 x y'$ .

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Step 5.2.1

Factor $y'$ out of $2 y y'$ .

$y' (2 y) - 3 x y' = - 2 x + 3 y$

Step 5.2.2

Factor $y'$ out of $- 3 x y'$ .

$y' (2 y) + y' (- 3 x) = - 2 x + 3 y$

Step 5.2.3

Factor $y'$ out of $y' (2 y) + y' (- 3 x)$ .

$y' (2 y - 3 x) = - 2 x + 3 y$

Step 5.3

Divide each term in $y' (2 y - 3 x) = - 2 x + 3 y$ by $2 y - 3 x$ and simplify.

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Step 5.3.1

Divide each term in $y' (2 y - 3 x) = - 2 x + 3 y$ by $2 y - 3 x$ .

$\frac{y' (2 y - 3 x)}{2 y - 3 x} = \frac{- 2 x}{2 y - 3 x} + \frac{3 y}{2 y - 3 x}$

Step 5.3.2

Simplify the left side.

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Step 5.3.2.1

Cancel the common factor of $2 y - 3 x$ .

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Step 5.3.2.1.1

Cancel the common factor.

$\frac{y' (2 y - 3 x)}{2 y - 3 x} = \frac{- 2 x}{2 y - 3 x} + \frac{3 y}{2 y - 3 x}$

Step 5.3.2.1.2

Divide $y'$ by $1$ .

$y' = \frac{- 2 x}{2 y - 3 x} + \frac{3 y}{2 y - 3 x}$

Step 5.3.3

Simplify the right side.

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Step 5.3.3.1

Combine the numerators over the common denominator.

$y' = \frac{- 2 x + 3 y}{2 y - 3 x}$

Step 5.3.3.2

Factor $- 1$ out of $- 2 x$ .

$y' = \frac{- (2 x) + 3 y}{2 y - 3 x}$

Step 5.3.3.3

Factor $- 1$ out of $3 y$ .

$y' = \frac{- (2 x) - (- 3 y)}{2 y - 3 x}$

Step 5.3.3.4

Factor $- 1$ out of $- (2 x) - (- 3 y)$ .

$y' = \frac{- (2 x - 3 y)}{2 y - 3 x}$

Step 5.3.3.5

Simplify the expression.

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Step 5.3.3.5.1

Rewrite $- (2 x - 3 y)$ as $- 1 (2 x - 3 y)$ .

$y' = \frac{- 1 (2 x - 3 y)}{2 y - 3 x}$

Step 5.3.3.5.2

Move the negative in front of the fraction.

$y' = - \frac{2 x - 3 y}{2 y - 3 x}$

Step 6

Replace $y'$ with $\frac{d y}{d x}$ .

$\frac{d y}{d x} = - \frac{2 x - 3 y}{2 y - 3 x}$

Step 7

Set $\frac{d y}{d x} = 0$ then solve for $x$ in terms of $y$ .

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Step 7.1

Set the numerator equal to zero.

$2 x - 3 y = 0$

Step 7.2

Solve the equation for $x$ .

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Step 7.2.1

Add $3 y$ to both sides of the equation.

$2 x = 3 y$

Step 7.2.2

Divide each term in $2 x = 3 y$ by $2$ and simplify.

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Step 7.2.2.1

Divide each term in $2 x = 3 y$ by $2$ .

$\frac{2 x}{2} = \frac{3 y}{2}$

Step 7.2.2.2

Simplify the left side.

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Step 7.2.2.2.1

Cancel the common factor of $2$ .

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Step 7.2.2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{3 y}{2}$

Step 7.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{3 y}{2}$

Step 8

Solve for $y$ .

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Step 8.1

Simplify $y^{2} - 3 \frac{3 y}{2} \cdot y + {(\frac{3 y}{2})}^{2}$ .

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Step 8.1.1

Simplify each term.

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Step 8.1.1.1

Multiply $- 3 \frac{3 y}{2}$ .

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Step 8.1.1.1.1

Combine $- 3$ and $\frac{3 y}{2}$ .

$y^{2} + \frac{- 3 (3 y)}{2} \cdot y + {(\frac{3 y}{2})}^{2} = 7$

Step 8.1.1.1.2

Multiply $3$ by $- 3$ .

$y^{2} + \frac{- 9 y}{2} \cdot y + {(\frac{3 y}{2})}^{2} = 7$

Step 8.1.1.2

Move the negative in front of the fraction.

$y^{2} - \frac{9 y}{2} \cdot y + {(\frac{3 y}{2})}^{2} = 7$

Step 8.1.1.3

Multiply $- \frac{9 y}{2} y$ .

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Step 8.1.1.3.1

Combine $y$ and $\frac{9 y}{2}$ .

$y^{2} - \frac{y (9 y)}{2} + {(\frac{3 y}{2})}^{2} = 7$

Step 8.1.1.3.2

Raise $y$ to the power of $1$ .

$y^{2} - \frac{9 (y^{1} y)}{2} + {(\frac{3 y}{2})}^{2} = 7$

Step 8.1.1.3.3

Raise $y$ to the power of $1$ .

$y^{2} - \frac{9 (y^{1} y^{1})}{2} + {(\frac{3 y}{2})}^{2} = 7$

Step 8.1.1.3.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$y^{2} - \frac{9 y^{1 + 1}}{2} + {(\frac{3 y}{2})}^{2} = 7$

Step 8.1.1.3.5

Add $1$ and $1$ .

$y^{2} - \frac{9 y^{2}}{2} + {(\frac{3 y}{2})}^{2} = 7$

Step 8.1.1.4

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 8.1.1.4.1

Apply the product rule to $\frac{3 y}{2}$ .

$y^{2} - \frac{9 y^{2}}{2} + \frac{{(3 y)}^{2}}{2^{2}} = 7$

Step 8.1.1.4.2

Apply the product rule to $3 y$ .

$y^{2} - \frac{9 y^{2}}{2} + \frac{3^{2} y^{2}}{2^{2}} = 7$

Step 8.1.1.5

Raise $3$ to the power of $2$ .

$y^{2} - \frac{9 y^{2}}{2} + \frac{9 y^{2}}{2^{2}} = 7$

Step 8.1.1.6

Raise $2$ to the power of $2$ .

$y^{2} - \frac{9 y^{2}}{2} + \frac{9 y^{2}}{4} = 7$

Step 8.1.2

Find the common denominator.

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Step 8.1.2.1

Write $y^{2}$ as a fraction with denominator $1$ .

$\frac{y^{2}}{1} - \frac{9 y^{2}}{2} + \frac{9 y^{2}}{4} = 7$

Step 8.1.2.2

Multiply $\frac{y^{2}}{1}$ by $\frac{4}{4}$ .

$\frac{y^{2}}{1} \cdot \frac{4}{4} - \frac{9 y^{2}}{2} + \frac{9 y^{2}}{4} = 7$

Step 8.1.2.3

Multiply $\frac{y^{2}}{1}$ by $\frac{4}{4}$ .

$\frac{y^{2} \cdot 4}{4} - \frac{9 y^{2}}{2} + \frac{9 y^{2}}{4} = 7$

Step 8.1.2.4

Multiply $\frac{9 y^{2}}{2}$ by $\frac{2}{2}$ .

$\frac{y^{2} \cdot 4}{4} - (\frac{9 y^{2}}{2} \cdot \frac{2}{2}) + \frac{9 y^{2}}{4} = 7$

Step 8.1.2.5

Multiply $\frac{9 y^{2}}{2}$ by $\frac{2}{2}$ .

$\frac{y^{2} \cdot 4}{4} - \frac{9 y^{2} \cdot 2}{2 \cdot 2} + \frac{9 y^{2}}{4} = 7$

Step 8.1.2.6

Multiply $2$ by $2$ .

$\frac{y^{2} \cdot 4}{4} - \frac{9 y^{2} \cdot 2}{4} + \frac{9 y^{2}}{4} = 7$

Step 8.1.3

Combine the numerators over the common denominator.

$\frac{y^{2} \cdot 4 - 9 y^{2} \cdot 2 + 9 y^{2}}{4} = 7$

Step 8.1.4

Simplify each term.

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Step 8.1.4.1

Move $4$ to the left of $y^{2}$ .

$\frac{4 \cdot y^{2} - 9 y^{2} \cdot 2 + 9 y^{2}}{4} = 7$

Step 8.1.4.2

Multiply $2$ by $- 9$ .

$\frac{4 y^{2} - 18 y^{2} + 9 y^{2}}{4} = 7$

Step 8.1.5

Simplify by adding terms.

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Step 8.1.5.1

Subtract $18 y^{2}$ from $4 y^{2}$ .

$\frac{- 14 y^{2} + 9 y^{2}}{4} = 7$

Step 8.1.5.2

Add $- 14 y^{2}$ and $9 y^{2}$ .

$\frac{- 5 y^{2}}{4} = 7$

Step 8.1.5.3

Move the negative in front of the fraction.

$- \frac{5 y^{2}}{4} = 7$

Step 8.2

Multiply both sides of the equation by $- \frac{4}{5}$ .

$- \frac{4}{5} (- \frac{5 y^{2}}{4}) = - \frac{4}{5} \cdot 7$

Step 8.3

Simplify both sides of the equation.

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Step 8.3.1

Simplify the left side.

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Step 8.3.1.1

Simplify $- \frac{4}{5} (- \frac{5 y^{2}}{4})$ .

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Step 8.3.1.1.1

Cancel the common factor of $4$ .

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Step 8.3.1.1.1.1

Move the leading negative in $- \frac{4}{5}$ into the numerator.

$\frac{- 4}{5} (- \frac{5 y^{2}}{4}) = - \frac{4}{5} \cdot 7$

Step 8.3.1.1.1.2

Move the leading negative in $- \frac{5 y^{2}}{4}$ into the numerator.

$\frac{- 4}{5} \cdot \frac{- 5 y^{2}}{4} = - \frac{4}{5} \cdot 7$

Step 8.3.1.1.1.3

Factor $4$ out of $- 4$ .

$\frac{4 (- 1)}{5} \cdot \frac{- 5 y^{2}}{4} = - \frac{4}{5} \cdot 7$

Step 8.3.1.1.1.4

Cancel the common factor.

$\frac{4 \cdot - 1}{5} \cdot \frac{- 5 y^{2}}{4} = - \frac{4}{5} \cdot 7$

Step 8.3.1.1.1.5

Rewrite the expression.

$\frac{- 1}{5} (- 5 y^{2}) = - \frac{4}{5} \cdot 7$

Step 8.3.1.1.2

Cancel the common factor of $5$ .

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Step 8.3.1.1.2.1

Factor $5$ out of $- 5 y^{2}$ .

$\frac{- 1}{5} (5 (- y^{2})) = - \frac{4}{5} \cdot 7$

Step 8.3.1.1.2.2

Cancel the common factor.

$\frac{- 1}{5} (5 (- y^{2})) = - \frac{4}{5} \cdot 7$

Step 8.3.1.1.2.3

Rewrite the expression.

$- - y^{2} = - \frac{4}{5} \cdot 7$

Step 8.3.1.1.3

Multiply.

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Step 8.3.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 y^{2} = - \frac{4}{5} \cdot 7$

Step 8.3.1.1.3.2

Multiply $y^{2}$ by $1$ .

$y^{2} = - \frac{4}{5} \cdot 7$

Step 8.3.2

Simplify the right side.

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Step 8.3.2.1

Simplify $- \frac{4}{5} \cdot 7$ .

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Step 8.3.2.1.1

Multiply $- \frac{4}{5} \cdot 7$ .

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Step 8.3.2.1.1.1

Multiply $7$ by $- 1$ .

$y^{2} = - 7 (\frac{4}{5})$

Step 8.3.2.1.1.2

Combine $- 7$ and $\frac{4}{5}$ .

$y^{2} = \frac{- 7 \cdot 4}{5}$

Step 8.3.2.1.1.3

Multiply $- 7$ by $4$ .

$y^{2} = \frac{- 28}{5}$

Step 8.3.2.1.2

Move the negative in front of the fraction.

$y^{2} = - \frac{28}{5}$

Step 8.4

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$y = \pm \sqrt{- \frac{28}{5}}$

Step 8.5

Simplify $\pm \sqrt{- \frac{28}{5}}$ .

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Step 8.5.1

Rewrite $- 1$ as $i^{2}$ .

$y = \pm \sqrt{i^{2} \frac{28}{5}}$

Step 8.5.2

Pull terms out from under the radical.

$y = \pm i \sqrt{\frac{28}{5}}$

Step 8.5.3

Rewrite $\sqrt{\frac{28}{5}}$ as $\frac{\sqrt{28}}{\sqrt{5}}$ .

$y = \pm i \frac{\sqrt{28}}{\sqrt{5}}$

Step 8.5.4

Simplify the numerator.

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Step 8.5.4.1

Rewrite $28$ as $2^{2} \cdot 7$ .

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Step 8.5.4.1.1

Factor $4$ out of $28$ .

$y = \pm i \frac{\sqrt{4 (7)}}{\sqrt{5}}$

Step 8.5.4.1.2

Rewrite $4$ as $2^{2}$ .

$y = \pm i \frac{\sqrt{2^{2} \cdot 7}}{\sqrt{5}}$

Step 8.5.4.2

Pull terms out from under the radical.

$y = \pm i \frac{2 \sqrt{7}}{\sqrt{5}}$

Step 8.5.5

Multiply $\frac{2 \sqrt{7}}{\sqrt{5}}$ by $\frac{\sqrt{5}}{\sqrt{5}}$ .

$y = \pm i (\frac{2 \sqrt{7}}{\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}})$

Step 8.5.6

Combine and simplify the denominator.

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Step 8.5.6.1

Multiply $\frac{2 \sqrt{7}}{\sqrt{5}}$ by $\frac{\sqrt{5}}{\sqrt{5}}$ .

$y = \pm i \frac{2 \sqrt{7} \sqrt{5}}{\sqrt{5} \sqrt{5}}$

Step 8.5.6.2

Raise $\sqrt{5}$ to the power of $1$ .

$y = \pm i \frac{2 \sqrt{7} \sqrt{5}}{{\sqrt{5}}^{1} \sqrt{5}}$

Step 8.5.6.3

Raise $\sqrt{5}$ to the power of $1$ .

$y = \pm i \frac{2 \sqrt{7} \sqrt{5}}{{\sqrt{5}}^{1} {\sqrt{5}}^{1}}$

Step 8.5.6.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$y = \pm i \frac{2 \sqrt{7} \sqrt{5}}{{\sqrt{5}}^{1 + 1}}$

Step 8.5.6.5

Add $1$ and $1$ .

$y = \pm i \frac{2 \sqrt{7} \sqrt{5}}{{\sqrt{5}}^{2}}$

Step 8.5.6.6

Rewrite ${\sqrt{5}}^{2}$ as $5$ .

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Step 8.5.6.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5}$ as $5^{\frac{1}{2}}$ .

$y = \pm i \frac{2 \sqrt{7} \sqrt{5}}{{(5^{\frac{1}{2}})}^{2}}$

Step 8.5.6.6.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$y = \pm i \frac{2 \sqrt{7} \sqrt{5}}{5^{\frac{1}{2} \cdot 2}}$

Step 8.5.6.6.3

Combine $\frac{1}{2}$ and $2$ .

$y = \pm i \frac{2 \sqrt{7} \sqrt{5}}{5^{\frac{2}{2}}}$

Step 8.5.6.6.4

Cancel the common factor of $2$ .

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Step 8.5.6.6.4.1

Cancel the common factor.

$y = \pm i \frac{2 \sqrt{7} \sqrt{5}}{5^{\frac{2}{2}}}$

Step 8.5.6.6.4.2

Rewrite the expression.

$y = \pm i \frac{2 \sqrt{7} \sqrt{5}}{5^{1}}$

Step 8.5.6.6.5

Evaluate the exponent.

$y = \pm i \frac{2 \sqrt{7} \sqrt{5}}{5}$

Step 8.5.7

Simplify the numerator.

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Step 8.5.7.1

Combine using the product rule for radicals.

$y = \pm i \frac{2 \sqrt{5 \cdot 7}}{5}$

Step 8.5.7.2

Multiply $5$ by $7$ .

$y = \pm i \frac{2 \sqrt{35}}{5}$

Step 8.5.8

Combine fractions.

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Step 8.5.8.1

Combine $i$ and $\frac{2 \sqrt{35}}{5}$ .

$y = \pm \frac{i (2 \sqrt{35})}{5}$

Step 8.5.8.2

Move $2$ to the left of $i$ .

$y = \pm \frac{2 i \sqrt{35}}{5}$

Step 8.6

The complete solution is the result of both the positive and negative portions of the solution.

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Step 8.6.1

First, use the positive value of the $\pm$ to find the first solution.

$y = \frac{2 i \sqrt{35}}{5}$

Step 8.6.2

Next, use the negative value of the $\pm$ to find the second solution.

$y = - \frac{2 i \sqrt{35}}{5}$

Step 8.6.3

The complete solution is the result of both the positive and negative portions of the solution.

$y = \frac{2 i \sqrt{35}}{5}, - \frac{2 i \sqrt{35}}{5}$

Step 9

Solve for $x$ when $y$ is $\frac{2 i \sqrt{35}}{5}$ .

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Step 9.1

Multiply $3$ by $\frac{2 i \sqrt{35}}{5}$ .

$x = \frac{3 (\frac{2 i \sqrt{35}}{5})}{2}$

Step 9.2

Simplify $\frac{3 (\frac{2 i \sqrt{35}}{5})}{2}$ .

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Step 9.2.1

Combine $3$ and $\frac{2 i \sqrt{35}}{5}$ .

$x = \frac{\frac{3 (2 i \sqrt{35})}{5}}{2}$

Step 9.2.2

Multiply $3$ by $2$ .

$x = \frac{\frac{6 i \sqrt{35}}{5}}{2}$

Step 9.2.3

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{6 i \sqrt{35}}{5} \cdot \frac{1}{2}$

Step 9.2.4

Cancel the common factor of $2$ .

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Step 9.2.4.1

Factor $2$ out of $6 i \sqrt{35}$ .

$x = \frac{2 (3 i \sqrt{35})}{5} \cdot \frac{1}{2}$

Step 9.2.4.2

Cancel the common factor.

$x = \frac{2 (3 i \sqrt{35})}{5} \cdot \frac{1}{2}$

Step 9.2.4.3

Rewrite the expression.

$x = \frac{3 i \sqrt{35}}{5}$

Step 10

Simplify $\frac{3 (- \frac{2 i \sqrt{35}}{5})}{2}$ .

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Step 10.1

Simplify the numerator.

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Step 10.1.1

Multiply $- 1$ by $3$ .

$x = \frac{- 3 \frac{2 i \sqrt{35}}{5}}{2}$

Step 10.1.2

Combine $- 3$ and $\frac{2 i \sqrt{35}}{5}$ .

$x = \frac{\frac{- 3 (2 i \sqrt{35})}{5}}{2}$

Step 10.2

Multiply $- 3$ by $2$ .

$x = \frac{\frac{- 6 i \sqrt{35}}{5}}{2}$

Step 10.3

Move the negative in front of the fraction.

$x = \frac{- \frac{6 i \sqrt{35}}{5}}{2}$

Step 10.4

Multiply the numerator by the reciprocal of the denominator.

$x = - \frac{6 i \sqrt{35}}{5} \cdot \frac{1}{2}$

Step 10.5

Cancel the common factor of $2$ .

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Step 10.5.1

Move the leading negative in $- \frac{6 i \sqrt{35}}{5}$ into the numerator.

$x = \frac{- 6 i \sqrt{35}}{5} \cdot \frac{1}{2}$

Step 10.5.2

Factor $2$ out of $- 6 i \sqrt{35}$ .

$x = \frac{2 (- 3 i \sqrt{35})}{5} \cdot \frac{1}{2}$

Step 10.5.3

Cancel the common factor.

$x = \frac{2 (- 3 i \sqrt{35})}{5} \cdot \frac{1}{2}$

Step 10.5.4

Rewrite the expression.

$x = \frac{- 3 i \sqrt{35}}{5}$

Step 10.6

Move the negative in front of the fraction.

$x = - \frac{3 i \sqrt{35}}{5}$

Step 11

Find the points where $\frac{d y}{d x} = 0$ .

$(\frac{3 i \sqrt{35}}{5}, \frac{2 i \sqrt{35}}{5})$

$(- \frac{3 i \sqrt{35}}{5}, - \frac{2 i \sqrt{35}}{5})$

Step 12