Calculus Examples

$r (x) = 7 + x^{2}$

Step 1

By the Sum Rule, the derivative of $7 + x^{2}$ with respect to $x$ is $\frac{d}{d x} [7] + \frac{d}{d x} [x^{2}]$ .

$\frac{d}{d x} [7] + \frac{d}{d x} [x^{2}]$

Step 2

Since $7$ is constant with respect to $x$ , the derivative of $7$ with respect to $x$ is $0$ .

$0 + \frac{d}{d x} [x^{2}]$

Step 3

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

$0 + 2 x$

Step 4

Add $0$ and $2 x$ .

$2 x$