Calculus Examples

$g (x) = \cos (x) - 5 \sin (x)$

Step 1

By the Sum Rule, the derivative of $\cos (x) - 5 \sin (x)$ with respect to $x$ is $\frac{d}{d x} [\cos (x)] + \frac{d}{d x} [- 5 \sin (x)]$ .

$\frac{d}{d x} [\cos (x)] + \frac{d}{d x} [- 5 \sin (x)]$

Step 2

The derivative of $\cos (x)$ with respect to $x$ is $- \sin (x)$ .

$- \sin (x) + \frac{d}{d x} [- 5 \sin (x)]$

Step 3

Evaluate $\frac{d}{d x} [- 5 \sin (x)]$ .

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Step 3.1

Since $- 5$ is constant with respect to $x$ , the derivative of $- 5 \sin (x)$ with respect to $x$ is $- 5 \frac{d}{d x} [\sin (x)]$ .

$- \sin (x) - 5 \frac{d}{d x} [\sin (x)]$

Step 3.2

The derivative of $\sin (x)$ with respect to $x$ is $\cos (x)$ .

$- \sin (x) - 5 \cos (x)$