Calculus Examples

$y = x + 4 y + 3 x$

Step 1

Solve for $y$ .

Tap for more steps...

Step 1.1

Add $x$ and $3 x$ .

$y = 4 x + 4 y$

Step 1.2

Move all terms containing $y$ to the left side of the equation.

Tap for more steps...

Step 1.2.1

Subtract $4 y$ from both sides of the equation.

$y - 4 y = 4 x$

Step 1.2.2

Subtract $4 y$ from $y$ .

$- 3 y = 4 x$

Step 1.3

Divide each term in $- 3 y = 4 x$ by $- 3$ and simplify.

Tap for more steps...

Step 1.3.1

Divide each term in $- 3 y = 4 x$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{4 x}{- 3}$

Step 1.3.2

Simplify the left side.

Tap for more steps...

Step 1.3.2.1

Cancel the common factor of $- 3$ .

Tap for more steps...

Step 1.3.2.1.1

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{4 x}{- 3}$

Step 1.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{4 x}{- 3}$

Step 1.3.3

Simplify the right side.

Tap for more steps...

Step 1.3.3.1

Move the negative in front of the fraction.

$y = - \frac{4 x}{3}$

Step 2

Find the first derivative.

Tap for more steps...

Step 2.1

Find the first derivative.

Tap for more steps...

Step 2.1.1

Since $- \frac{4}{3}$ is constant with respect to $x$ , the derivative of $- \frac{4 x}{3}$ with respect to $x$ is $- \frac{4}{3} \frac{d}{d x} [x]$ .

$- \frac{4}{3} \frac{d}{d x} [x]$

Step 2.1.2

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

$- \frac{4}{3} \cdot 1$

Step 2.1.3

Multiply $- 1$ by $1$ .

$f' (x) = - \frac{4}{3}$

Step 2.2

The first derivative of $f (x)$ with respect to $x$ is $- \frac{4}{3}$ .

$- \frac{4}{3}$

Step 3

Set the first derivative equal to $0$ then solve the equation $- \frac{4}{3} = 0$ .

Tap for more steps...

Step 3.1

Set the first derivative equal to $0$ .

$- \frac{4}{3} = 0$

Step 3.2

Set the numerator equal to zero.

$4 = 0$

Step 3.3

Since $4 \neq 0$ , there are no solutions.

No solution

Step 4

There are no values of $x$ in the domain of the original problem where the derivative is $0$ or undefined.

No critical points found