Calculus Examples

$f (x) = 7 \sin (x) - 7 \sqrt{3} \cos (x^{0})$

Step 1

By the Sum Rule, the derivative of $7 \sin (x) - 7 \sqrt{3} \cos (x^{0})$ with respect to $x$ is $\frac{d}{d x} [7 \sin (x)] + \frac{d}{d x} [- 7 \sqrt{3} \cos (x^{0})]$ .

$\frac{d}{d x} [7 \sin (x)] + \frac{d}{d x} [- 7 \sqrt{3} \cos (x^{0})]$

Step 2

Evaluate $\frac{d}{d x} [7 \sin (x)]$ .

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Step 2.1

Since $7$ is constant with respect to $x$ , the derivative of $7 \sin (x)$ with respect to $x$ is $7 \frac{d}{d x} [\sin (x)]$ .

$7 \frac{d}{d x} [\sin (x)] + \frac{d}{d x} [- 7 \sqrt{3} \cos (x^{0})]$

Step 2.2

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

$7 \cos (x) + \frac{d}{d x} [- 7 \sqrt{3} \cos (x^{0})]$

Step 3

Evaluate $\frac{d}{d x} [- 7 \sqrt{3} \cos (x^{0})]$ .

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Step 3.1

Anything raised to $0$ is $1$ .

$7 \cos (x) + \frac{d}{d x} [- 7 \sqrt{3} \cos (1)]$

Step 3.2

Since $- 7 \sqrt{3} \cos (1)$ is constant with respect to $x$ , the derivative of $- 7 \sqrt{3} \cos (1)$ with respect to $x$ is $0$ .

$7 \cos (x) + 0$

Step 4

Add $7 \cos (x)$ and $0$ .

$7 \cos (x)$