Calculus Examples

$2 \cos (x) + x$

Step 1

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

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

Step 2

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

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

Multiply $- 1$ by $2$ .

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

Step 3

Differentiate using the Power Rule.

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Step 3.1

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 1$ .

$- 2 \sin (x) + 1$

Step 3.2

Reorder terms.

$1 - 2 \sin (x)$