Calculus Examples

$y = - 7 x^{8} - 3$

Step 1

By the Sum Rule, the derivative of $- 7 x^{8} - 3$ with respect to $x$ is $\frac{d}{d x} [- 7 x^{8}] + \frac{d}{d x} [- 3]$ .

$\frac{d}{d x} [- 7 x^{8}] + \frac{d}{d x} [- 3]$

Step 2

Evaluate $\frac{d}{d x} [- 7 x^{8}]$ .

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Step 2.1

Since $- 7$ is constant with respect to $x$ , the derivative of $- 7 x^{8}$ with respect to $x$ is $- 7 \frac{d}{d x} [x^{8}]$ .

$- 7 \frac{d}{d x} [x^{8}] + \frac{d}{d x} [- 3]$

Step 2.2

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 8$ .

$- 7 (8 x^{7}) + \frac{d}{d x} [- 3]$

Step 2.3

Multiply $8$ by $- 7$ .

$- 56 x^{7} + \frac{d}{d x} [- 3]$

Step 3

Differentiate using the Constant Rule.

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Step 3.1

Since $- 3$ is constant with respect to $x$ , the derivative of $- 3$ with respect to $x$ is $0$ .

$- 56 x^{7} + 0$

Step 3.2

Add $- 56 x^{7}$ and $0$ .

$- 56 x^{7}$