Calculus Examples

$\cos (x)$

Step 1

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

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

Step 2

Find the second derivative.

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

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

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

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

Step 3

Find the third derivative.

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

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

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

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

Multiply.

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Multiply $- 1$ by $- 1$ .

$f''' (x) = 1 \sin (x)$

Multiply $\sin (x)$ by $1$ .

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