Calculus Examples

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

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

Step 1

Since

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

$- \frac{1}{y^{2}}$ is constant with respect to

x

$x$ , the derivative of

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

$- \frac{x^{2}}{y^{2}}$ with respect to

x

$x$ is

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

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

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

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

Step 2

Differentiate using the Power Rule which states that

\frac{d}{d x} [x^{n}]

$\frac{d}{d x} [x^{n}]$ is

n x^{n - 1}

$n x^{n - 1}$ where

n = 2

$n = 2$ .

- \frac{1}{y^{2}} (2 x)

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

Step 3

Combine fractions.

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Step 3.1

Multiply

2

$2$ by

- 1

$- 1$ .

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

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

Step 3.2

Combine

- 2

$- 2$ and

\frac{1}{y^{2}}

$\frac{1}{y^{2}}$ .

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

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

Step 3.3

Combine

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

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

x

$x$ .

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

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

Step 3.4

Move the negative in front of the fraction.

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

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

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

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

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

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

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[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$