Calculus Examples

$f (x) = \log (10) (x^{3} + 1)$

Step 1

Logarithm base $10$ of $10$ is $1$ .

$\frac{d}{d x} [1 (x^{3} + 1)]$

Step 2

Multiply $x^{3} + 1$ by $1$ .

$\frac{d}{d x} [x^{3} + 1]$

Step 3

By the Sum Rule, the derivative of $x^{3} + 1$ with respect to $x$ is $\frac{d}{d x} [x^{3}] + \frac{d}{d x} [1]$ .

$\frac{d}{d x} [x^{3}] + \frac{d}{d x} [1]$

Step 4

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

$3 x^{2} + \frac{d}{d x} [1]$

Step 5

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

$3 x^{2} + 0$

Step 6

Add $3 x^{2}$ and $0$ .

$3 x^{2}$