Calculus Examples

$\sin (x) x^{2}$

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 $f (x) = \sin (x)$ and $g (x) = x^{2}$ .

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

Step 2

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 2$ .

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

Step 3

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

$\sin (x) (2 x) + x^{2} \cos (x)$

Step 4

Reorder terms.

$2 x \sin (x) + x^{2} \cos (x)$