Calculus Examples

$y = \csc (x) \tan (x)$

Step 1

Differentiate using the Product Rule which states that $\frac{d}{d x} [f (x) g (x)]$ is $f (x) \frac{d}{d x} [g (x)] + g (x) \frac{d}{d x} [f (x)]$ where $f (x) = \csc (x)$ and $g (x) = \tan (x)$ .

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

Step 2

The derivative of $\tan (x)$ with respect to $x$ is $\sec^{2} (x)$ .

$\csc (x) \sec^{2} (x) + \tan (x) \frac{d}{d x} [\csc (x)]$

Step 3

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

$\csc (x) \sec^{2} (x) + \tan (x) (- \csc (x) \cot (x))$

Step 4

Reorder terms.

$\sec^{2} (x) \csc (x) - \cot (x) \csc (x) \tan (x)$