Calculus Examples

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

Step 1

Differentiate.

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Step 1.1

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

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

Step 1.2

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

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

Step 2

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

$2 x + e^{x}$