Calculus Examples

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

Step 1

Differentiate using the chain rule, which states that $\frac{d}{d x} [f (g (x))]$ is $f' (g (x)) g' (x)$ where $f (x) = \tan (x)$ and $g (x) = \sec (x)$ .

Tap for more steps...

Step 1.1

To apply the Chain Rule, set $u$ as $\sec (x)$ .

$\frac{d}{d u} [\tan (u)] \frac{d}{d x} [\sec (x)]$

Step 1.2

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

$\sec^{2} (u) \frac{d}{d x} [\sec (x)]$

Step 1.3

Replace all occurrences of $u$ with $\sec (x)$ .

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

Step 2

The derivative of $\sec (x)$ with respect to $x$ is $\sec (x) \tan (x)$ .

$\sec^{2} (\sec (x)) \sec (x) \tan (x)$