Calculus Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

Simplify.

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Step 4.1

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

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

Step 4.2

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

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