Calculus Examples

$\frac{d}{d t} (\frac{{(4 t - 6)}^{9}}{t + 5})$

Step 1

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

Step 2

Simplify the numerator.

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Step 2.1

Factor $2$ out of $4 t - 6$ .

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Step 2.1.1

Factor $2$ out of $4 t$ .

$\frac{d}{d \cdot d} [\frac{{(2 (2 t) - 6)}^{9}}{t + 5}]$

Step 2.1.2

Factor $2$ out of $- 6$ .

$\frac{d}{d \cdot d} [\frac{{(2 (2 t) + 2 (- 3))}^{9}}{t + 5}]$

Step 2.1.3

Factor $2$ out of $2 (2 t) + 2 (- 3)$ .

$\frac{d}{d \cdot d} [\frac{{(2 (2 t - 3))}^{9}}{t + 5}]$

Step 2.2

Apply the product rule to $2 (2 t - 3)$ .

$\frac{d}{d \cdot d} [\frac{2^{9} {(2 t - 3)}^{9}}{t + 5}]$

Step 2.3

Raise $2$ to the power of $9$ .

$\frac{d}{d \cdot d} [\frac{512 {(2 t - 3)}^{9}}{t + 5}]$

Step 3

Since $\frac{512 {(2 t - 3)}^{9}}{t + 5}$ is constant with respect to $d$ , the derivative of $\frac{512 {(2 t - 3)}^{9}}{t + 5}$ with respect to $d$ is $0$ .

$0$