Calculus Examples

$\frac{d}{d x} (\cos (x) x^{2})$

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

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

Step 2

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

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

Step 3

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

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

Step 4

Reorder terms.

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