Calculus Examples

$\frac{2 y}{x}$

Step 1

Since $2 y$ is constant with respect to $x$ , the derivative of $\frac{2 y}{x}$ with respect to $x$ is $2 y \frac{d}{d x} [\frac{1}{x}]$ .

$2 y \frac{d}{d x} [\frac{1}{x}]$

Step 2

Rewrite $\frac{1}{x}$ as $x^{- 1}$ .

$2 y \frac{d}{d x} [x^{- 1}]$

Step 3

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

$2 y (- x^{- 2})$

Step 4

Multiply $- 1$ by $2$ .

$- 2 y x^{- 2}$

Step 5

Simplify.

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Step 5.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$- 2 y \frac{1}{x^{2}}$

Step 5.2

Combine terms.

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Step 5.2.1

Combine $- 2$ and $\frac{1}{x^{2}}$ .

$y \frac{- 2}{x^{2}}$

Step 5.2.2

Combine $y$ and $\frac{- 2}{x^{2}}$ .

$\frac{y \cdot - 2}{x^{2}}$

Step 5.2.3

Move $- 2$ to the left of $y$ .

$\frac{- 2 \cdot y}{x^{2}}$

Step 5.2.4

Move the negative in front of the fraction.

$- \frac{2 y}{x^{2}}$