Calculus Examples

$y = 7 + 6 \sin (x)$

Step 1

Differentiate.

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Step 1.1

By the Sum Rule, the derivative of $7 + 6 \sin (x)$ with respect to $x$ is $\frac{d}{d x} [7] + \frac{d}{d x} [6 \sin (x)]$ .

$\frac{d}{d x} [7] + \frac{d}{d x} [6 \sin (x)]$

Step 1.2

Since $7$ is constant with respect to $x$ , the derivative of $7$ with respect to $x$ is $0$ .

$0 + \frac{d}{d x} [6 \sin (x)]$

Step 2

Evaluate $\frac{d}{d x} [6 \sin (x)]$ .

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Step 2.1

Since $6$ is constant with respect to $x$ , the derivative of $6 \sin (x)$ with respect to $x$ is $6 \frac{d}{d x} [\sin (x)]$ .

$0 + 6 \frac{d}{d x} [\sin (x)]$

Step 2.2

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

$0 + 6 \cos (x)$

Step 3

Add $0$ and $6 \cos (x)$ .

$6 \cos (x)$