Calculus Examples

$f (x) = x^{3} + 4 x$ , $c = 7$

Step 1

Differentiate.

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Step 1.1

By the Sum Rule, the derivative of $x^{3} + 4 x$ with respect to $x$ is $\frac{d}{d x} [x^{3}] + \frac{d}{d x} [4 x]$ .

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

Step 1.2

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 3$ .

$3 x^{2} + \frac{d}{d x} [4 x]$

Step 2

Evaluate $\frac{d}{d x} [4 x]$ .

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Step 2.1

Since $4$ is constant with respect to $x$ , the derivative of $4 x$ with respect to $x$ is $4 \frac{d}{d x} [x]$ .

$3 x^{2} + 4 \frac{d}{d x} [x]$

Step 2.2

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

$3 x^{2} + 4 \cdot 1$

Step 2.3

Multiply $4$ by $1$ .

$3 x^{2} + 4$