Calculus Examples

5 x^{3}

$5 x^{3}$

Step 1

Since

5

$5$ is constant with respect to

x

$x$ , the derivative of

5 x^{3}

$5 x^{3}$ with respect to

x

$x$ is

5 \frac{d}{d x} [x^{3}]

$5 \frac{d}{d x} [x^{3}]$ .

5 \frac{d}{d x} [x^{3}]

$5 \frac{d}{d x} [x^{3}]$

Step 2

Differentiate using the Power Rule which states that

\frac{d}{d x} [x^{n}]

$\frac{d}{d x} [x^{n}]$ is

n x^{n - 1}

$n x^{n - 1}$ where

n = 3

$n = 3$ .

5 (3 x^{2})

$5 (3 x^{2})$

Step 3

Multiply

3

$3$ by

5

$5$ .

15 x^{2}

$15 x^{2}$

5 x^{3}

$5 x^{3}$

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