Calculus Examples

$| \sin (x) |$

Step 1

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

Tap for more steps...

Step 1.1

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

$\frac{d}{d u} [| u |] \frac{d}{d x} [\sin (x)]$

Step 1.2

The derivative of $| u |$ with respect to $u$ is $\frac{u}{| u |}$ .

$\frac{u}{| u |} \frac{d}{d x} [\sin (x)]$

Step 1.3

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

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

Step 2

The derivative of $\sin (x)$ with respect to $x$ is $\cos (x)$ .

$\frac{\sin (x)}{| \sin (x) |} \cos (x)$

Step 3

Combine fractions.

Tap for more steps...

Step 3.1

Combine $\frac{\sin (x)}{| \sin (x) |}$ and $\cos (x)$ .

$\frac{\sin (x) \cos (x)}{| \sin (x) |}$

Step 3.2

Reorder terms.

$\frac{\cos (x) \sin (x)}{| \sin (x) |}$