Calculus Examples

sin (x)

$\sin (x)$

Step 1

The derivative of

sin (x)

$\sin (x)$ with respect to

x

$x$ is

cos (x)

$\cos (x)$ .

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

Step 2

The derivative of

$\cos (x)$ with respect to

$x$ is

$- \sin (x)$ .

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

Step 3

Find the third derivative.

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Step 3.1

Since

$- 1$ is constant with respect to

$x$ , the derivative of

$- \sin (x)$ with respect to

$x$ is

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

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

Step 3.2

The derivative of

$\sin (x)$ with respect to

$x$ is

$\cos (x)$ .

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

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

Step 4

Find the fourth derivative.

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Step 4.1

Since

$- 1$ is constant with respect to

$x$ , the derivative of

$- \cos (x)$ with respect to

$x$ is

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

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

Step 4.2

The derivative of

$\cos (x)$ with respect to

$x$ is

$- \sin (x)$ .

$- - \sin (x)$

Step 4.3

Multiply.

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Step 4.3.1

Multiply

$- 1$ by

$- 1$ .

$1 \sin (x)$

Step 4.3.2

Multiply

$\sin (x)$ by

$1$ .

$f^{4} (x) = \sin (x)$

$f^{4} (x) = \sin (x)$

$f^{4} (x) = \sin (x)$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$