Calculus Examples

$x^{2} - 8 \ln (x)$

Step 1

Differentiate.

Tap for more steps...

Step 1.1

By the Sum Rule, the derivative of $x^{2} - 8 \ln (x)$ with respect to $x$ is $\frac{d}{d x} [x^{2}] + \frac{d}{d x} [- 8 \ln (x)]$ .

$\frac{d}{d x} [x^{2}] + \frac{d}{d x} [- 8 \ln (x)]$

Step 1.2

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

$2 x + \frac{d}{d x} [- 8 \ln (x)]$

Step 2

Evaluate $\frac{d}{d x} [- 8 \ln (x)]$ .

Tap for more steps...

Step 2.1

Since $- 8$ is constant with respect to $x$ , the derivative of $- 8 \ln (x)$ with respect to $x$ is $- 8 \frac{d}{d x} [\ln (x)]$ .

$2 x - 8 \frac{d}{d x} [\ln (x)]$

Step 2.2

The derivative of $\ln (x)$ with respect to $x$ is $\frac{1}{x}$ .

$2 x - 8 \frac{1}{x}$

Step 2.3

Combine $- 8$ and $\frac{1}{x}$ .

$2 x + \frac{- 8}{x}$

Step 2.4

Move the negative in front of the fraction.

$2 x - \frac{8}{x}$