Calculus Examples

x^{3} + x^{2}

$x^{3} + x^{2}$

Step 1

By the Sum Rule, the derivative of

x^{3} + x^{2}

$x^{3} + x^{2}$ with respect to

x

$x$ is

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

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

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

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

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 = 3

$n = 3$ .

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

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

Step 3

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 x^{2} + 2 x

$3 x^{2} + 2 x$