Calculus Examples

$y = x^{4} + 8$

Step 1

By the Sum Rule, the derivative of $x^{4} + 8$ with respect to $x$ is $\frac{d}{d x} [x^{4}] + \frac{d}{d x} [8]$ .

$\frac{d}{d x} [x^{4}] + \frac{d}{d x} [8]$

Step 2

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 4$ .

$4 x^{3} + \frac{d}{d x} [8]$

Step 3

Since $8$ is constant with respect to $x$ , the derivative of $8$ with respect to $x$ is $0$ .

$4 x^{3} + 0$

Step 4

Add $4 x^{3}$ and $0$ .

$4 x^{3}$