Calculus Examples

$y = 1 - \sin (x)$

Step 1

Differentiate.

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Step 1.1

By the Sum Rule, the derivative of $1 - \sin (x)$ with respect to $x$ is $\frac{d}{d x} [1] + \frac{d}{d x} [- \sin (x)]$ .

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

Step 1.2

Since $1$ is constant with respect to $x$ , the derivative of $1$ with respect to $x$ is $0$ .

$0 + \frac{d}{d x} [- \sin (x)]$

Step 2

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

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Step 2.1

Since $- 1$ is constant with respect to $x$ , the derivative of $- \sin (x)$ with respect to $x$ is $- \frac{d}{d x} [\sin (x)]$ .

$0 - \frac{d}{d x} [\sin (x)]$

Step 2.2

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

$0 - \cos (x)$

Step 3

Subtract $\cos (x)$ from $0$ .

$- \cos (x)$