Calculus Examples

$\frac{7}{\sin (x)}$

Step 1

Since $7$ is constant with respect to $x$ , the derivative of $\frac{7}{\sin (x)}$ with respect to $x$ is $7 \frac{d}{d x} [\frac{1}{\sin (x)}]$ .

$7 \frac{d}{d x} [\frac{1}{\sin (x)}]$

Step 2

Convert from $\frac{1}{\sin (x)}$ to $\csc (x)$ .

$7 \frac{d}{d x} [\csc (x)]$

Step 3

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

$7 (- \csc (x) \cot (x))$

Step 4

Simplify the expression.

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Step 4.1

Multiply $- 1$ by $7$ .

$- 7 (\csc (x) \cot (x))$

Step 4.2

Reorder the factors of $- 7 \csc (x) \cot (x)$ .

$- 7 \cot (x) \csc (x)$