Calculus Examples

$y = x + \cos (x)$

Step 1

Differentiate.

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Step 1.1

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

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

Step 1.2

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

$1 + \frac{d}{d x} [\cos (x)]$

Step 2

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

$1 - \sin (x)$