Calculus Examples

f (x) = 3 x^{2}

$f (x) = 3 x^{2}$

Step 1

Since

3

$3$ is constant with respect to

x

$x$ , the derivative of

3 x^{2}

$3 x^{2}$ with respect to

x

$x$ is

3 \frac{d}{d x} [x^{2}]

$3 \frac{d}{d x} [x^{2}]$ .

3 \frac{d}{d x} [x^{2}]

$3 \frac{d}{d x} [x^{2}]$

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 = 2

$n = 2$ .

3 (2 x)

$3 (2 x)$

Step 3

Multiply

2

$2$ by

3

$3$ .

6 x

$6 x$

f (x) = 3 x^{2}

$f (x) = 3 x^{2}$

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