Calculus Examples

$q = \sqrt{12 r - r^{7}}$

Step 1

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

Step 2

Factor $r$ out of $12 r - r^{7}$ .

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Step 2.1

Factor $r$ out of $12 r$ .

$\frac{d}{d q} [\sqrt{r \cdot 12 - r^{7}}]$

Step 2.2

Factor $r$ out of $- r^{7}$ .

$\frac{d}{d q} [\sqrt{r \cdot 12 + r (- r^{6})}]$

Step 2.3

Factor $r$ out of $r \cdot 12 + r (- r^{6})$ .

$\frac{d}{d q} [\sqrt{r (12 - r^{6})}]$

Step 3

Since $\sqrt{r (12 - r^{6})}$ is constant with respect to $q$ , the derivative of $\sqrt{r (12 - r^{6})}$ with respect to $q$ is $0$ .

$0$