Calculus Examples

$- \frac{3 x}{4 y}$

Step 1

This derivative could not be completed using the quotient rule. Mathway will use another method.

Step 2

Since $- \frac{3 x}{4}$ is constant with respect to $y$ , the derivative of $- \frac{3 x}{4 y}$ with respect to $y$ is $- \frac{3 x}{4} \frac{d}{d y} [\frac{1}{y}]$ .

$- \frac{3 x}{4} \frac{d}{d y} [\frac{1}{y}]$

Step 3

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

$- \frac{3 x}{4} \frac{d}{d y} [y^{- 1}]$

Step 4

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

$- \frac{3 x}{4} (- y^{- 2})$

Step 5

Combine fractions.

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Step 5.1

Multiply $- 1$ by $- 1$ .

$1 \frac{3 x}{4} y^{- 2}$

Step 5.2

Multiply $\frac{3 x}{4}$ by $1$ .

$\frac{3 x}{4} y^{- 2}$

Step 5.3

Combine $\frac{3 x}{4}$ and $y^{- 2}$ .

$\frac{3 x y^{- 2}}{4}$

Step 5.4

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

$\frac{3 x}{4 y^{2}}$