Calculus Examples

$1 + \csc (x)$

Step 1

Differentiate.

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Step 1.1

By the Sum Rule, the derivative of $1 + \csc (x)$ with respect to $x$ is $\frac{d}{d x} [1] + \frac{d}{d x} [\csc (x)]$ .

$\frac{d}{d x} [1] + \frac{d}{d x} [\csc (x)]$

Step 1.2

Since $1$ is constant with respect to $x$ , the derivative of $1$ with respect to $x$ is $0$ .

$0 + \frac{d}{d x} [\csc (x)]$

Step 2

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

$0 - \csc (x) \cot (x)$

Step 3

Simplify.

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Step 3.1

Subtract $\csc (x) \cot (x)$ from $0$ .

$- \csc (x) \cot (x)$

Step 3.2

Reorder the factors of $- \csc (x) \cot (x)$ .

$- \cot (x) \csc (x)$