Calculus Examples

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

Step 1

Move the negative in front of the fraction.

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

Step 2

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

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

Step 3

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

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

Step 4

Combine fractions.

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Step 4.1

Multiply $2$ by $- 1$ .

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

Step 4.2

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

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

Step 4.3

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

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

Step 4.4

Move the negative in front of the fraction.

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