Calculus Examples

$3 x^{3}$

Step 1

Find the first derivative.

Tap for more steps...

Step 1.1

Since $3$ is constant with respect to $x$ , the derivative of $3 x^{3}$ with respect to $x$ is $3 \frac{d}{d x} [x^{3}]$ .

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

Step 1.2

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

$3 (3 x^{2})$

Step 1.3

Multiply $3$ by $3$ .

$f' (x) = 9 x^{2}$

Step 2

Find the second derivative.

Tap for more steps...

Step 2.1

Since $9$ is constant with respect to $x$ , the derivative of $9 x^{2}$ with respect to $x$ is $9 \frac{d}{d x} [x^{2}]$ .

$9 \frac{d}{d x} [x^{2}]$

Step 2.2

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

$9 (2 x)$

Step 2.3

Multiply $2$ by $9$ .

$f'' (x) = 18 x$

Enter YOUR Problem