Calculus Examples

$y = \sin^{6} (x) + \cos^{6} (x)$

Step 1

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

Step 2

By the Sum Rule, the derivative of $\sin^{6} (x) + \cos^{6} (x)$ with respect to $z$ is $\frac{d}{d z} [\sin^{6} (x)] + \frac{d}{d z} [\cos^{6} (x)]$ .

$\frac{d}{d z} [\sin^{6} (x)] + \frac{d}{d z} [\cos^{6} (x)]$

Step 3

Since $\sin^{6} (x)$ is constant with respect to $z$ , the derivative of $\sin^{6} (x)$ with respect to $z$ is $0$ .

$0 + \frac{d}{d z} [\cos^{6} (x)]$

Step 4

Since $\cos^{6} (x)$ is constant with respect to $z$ , the derivative of $\cos^{6} (x)$ with respect to $z$ is $0$ .

$0 + 0$

Step 5

Add $0$ and $0$ .

$0$