Calculus Examples

x^{3} + 1

$x^{3} + 1$

Step 1

By the Sum Rule, the derivative of

x^{3} + 1

$x^{3} + 1$ with respect to

x

$x$ is

\frac{d}{d x} [x^{3}] + \frac{d}{d x} [1]

$\frac{d}{d x} [x^{3}] + \frac{d}{d x} [1]$ .

\frac{d}{d x} [x^{3}] + \frac{d}{d x} [1]

$\frac{d}{d x} [x^{3}] + \frac{d}{d x} [1]$

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

$n = 3$ .

3 x^{2} + \frac{d}{d x} [1]

$3 x^{2} + \frac{d}{d x} [1]$

Step 3

Since

1

$1$ is constant with respect to

x

$x$ , the derivative of

1

$1$ with respect to

x

$x$ is

0

$0$ .

3 x^{2} + 0

$3 x^{2} + 0$

Step 4

Add

3 x^{2}

$3 x^{2}$ and

0

$0$ .

3 x^{2}

$3 x^{2}$

x^{3} + 1

$x^{3} + 1$

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