Calculus Examples

$e^{x} - \sqrt{e}$

Step 1

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

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

Step 2

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

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

Step 3

Differentiate using the Constant Rule.

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Step 3.1

Since $- \sqrt{e}$ is constant with respect to $x$ , the derivative of $- \sqrt{e}$ with respect to $x$ is $0$ .

$e^{x} + 0$

Step 3.2

Add $e^{x}$ and $0$ .

$e^{x}$