Calculus Examples

$4 \cos (x) + 2 \sin (x)$

Step 1

By the Sum Rule, the derivative of $4 \cos (x) + 2 \sin (x)$ with respect to $x$ is $\frac{d}{d x} [4 \cos (x)] + \frac{d}{d x} [2 \sin (x)]$ .

$\frac{d}{d x} [4 \cos (x)] + \frac{d}{d x} [2 \sin (x)]$

Step 2

Evaluate $\frac{d}{d x} [4 \cos (x)]$ .

Tap for more steps...

Step 2.1

Since $4$ is constant with respect to $x$ , the derivative of $4 \cos (x)$ with respect to $x$ is $4 \frac{d}{d x} [\cos (x)]$ .

$4 \frac{d}{d x} [\cos (x)] + \frac{d}{d x} [2 \sin (x)]$

Step 2.2

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

$4 (- \sin (x)) + \frac{d}{d x} [2 \sin (x)]$

Step 2.3

Multiply $- 1$ by $4$ .

$- 4 \sin (x) + \frac{d}{d x} [2 \sin (x)]$

Step 3

Evaluate $\frac{d}{d x} [2 \sin (x)]$ .

Tap for more steps...

Step 3.1

Since $2$ is constant with respect to $x$ , the derivative of $2 \sin (x)$ with respect to $x$ is $2 \frac{d}{d x} [\sin (x)]$ .

$- 4 \sin (x) + 2 \frac{d}{d x} [\sin (x)]$

Step 3.2

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

$- 4 \sin (x) + 2 \cos (x)$