Calculus Examples

$x^{3} + x$

Step 1

By the Sum Rule, the derivative of $x^{3} + x$ with respect to $x$ is $\frac{d}{d x} [x^{3}] + \frac{d}{d x} [x]$ .

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

Step 2

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 3$ .

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

Step 3

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 1$ .

$3 x^{2} + 1$