Calculus Examples

$\frac{x}{2 y}$

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

Combine fractions.

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Step 4.1

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

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

Step 4.2

Move $y^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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