Calculus Examples

$e^{x} - \cot (x)$

Step 1

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

$\frac{d}{d x} [e^{x}] + \frac{d}{d x} [- \cot (x)]$

Step 2

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

$e^{x} + \frac{d}{d x} [- \cot (x)]$

Step 3

Evaluate $\frac{d}{d x} [- \cot (x)]$ .

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Step 3.1

Since $- 1$ is constant with respect to $x$ , the derivative of $- \cot (x)$ with respect to $x$ is $- \frac{d}{d x} [\cot (x)]$ .

$e^{x} - \frac{d}{d x} [\cot (x)]$

Step 3.2

The derivative of $\cot (x)$ with respect to $x$ is $- \csc^{2} (x)$ .

$e^{x} - - \csc^{2} (x)$

Step 3.3

Multiply $- 1$ by $- 1$ .

$e^{x} + 1 \csc^{2} (x)$

Step 3.4

Multiply $\csc^{2} (x)$ by $1$ .

$e^{x} + \csc^{2} (x)$