Calculus Examples

$2 (x^{2} - 1)$

Step 1

Since $2$ is constant with respect to $x$ , the derivative of $2 (x^{2} - 1)$ with respect to $x$ is $2 \frac{d}{d x} [x^{2} - 1]$ .

$2 \frac{d}{d x} [x^{2} - 1]$

Step 2

By the Sum Rule, the derivative of $x^{2} - 1$ with respect to $x$ is $\frac{d}{d x} [x^{2}] + \frac{d}{d x} [- 1]$ .

$2 (\frac{d}{d x} [x^{2}] + \frac{d}{d x} [- 1])$

Step 3

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

$2 (2 x + \frac{d}{d x} [- 1])$

Step 4

Since $- 1$ is constant with respect to $x$ , the derivative of $- 1$ with respect to $x$ is $0$ .

$2 (2 x + 0)$

Step 5

Simplify the expression.

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Step 5.1

Add $2 x$ and $0$ .

$2 (2 x)$

Step 5.2

Multiply $2$ by $2$ .

$4 x$