Calculus Examples

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

Step 1

By the Sum Rule, the derivative of $2^{x} + x^{2}$ with respect to $x$ is $\frac{d}{d x} [2^{x}] + \frac{d}{d x} [x^{2}]$ .

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

Step 2

Differentiate using the Exponential Rule which states that $\frac{d}{d x} [a^{x}]$ is $a^{x} \ln (a)$ where $a$ = $2$ .

$2^{x} \ln (2) + \frac{d}{d x} [x^{2}]$

Step 3

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 2$ .

$2^{x} \ln (2) + 2 x$