Calculus Examples

$f (x) = 5 \cos (x)$

Find the first derivative.

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Since $5$ is constant with respect to $x$ , the derivative of $5 \cos (x)$ with respect to $x$ is $5 \frac{d}{d x} [\cos (x)]$ .

$f' (x) = 5 \frac{d}{d x} (\cos (x))$

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

$f' (x) = 5 (- \sin (x))$

Multiply $- 1$ by $5$ .

$f' (x) = - 5 \sin (x)$

Find the second derivative.

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Since $- 5$ is constant with respect to $x$ , the derivative of $- 5 \sin (x)$ with respect to $x$ is $- 5 \frac{d}{d x} [\sin (x)]$ .

$f'' (x) = - 5 \frac{d}{d x} \sin (x)$

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

$f'' (x) = - 5 \cos (x)$

The second derivative of $f (x)$ with respect to $x$ is $- 5 \cos (x)$ .

$- 5 \cos (x)$