Calculus Examples

$\frac{x^{4}}{6}$

Step 1

Since $\frac{1}{6}$ is constant with respect to $x$ , the derivative of $\frac{x^{4}}{6}$ with respect to $x$ is $\frac{1}{6} \frac{d}{d x} [x^{4}]$ .

$\frac{1}{6} \frac{d}{d x} [x^{4}]$

Step 2

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

$\frac{1}{6} (4 x^{3})$

Step 3

Simplify terms.

Tap for more steps...

Step 3.1

Combine $4$ and $\frac{1}{6}$ .

$\frac{4}{6} x^{3}$

Step 3.2

Combine $\frac{4}{6}$ and $x^{3}$ .

$\frac{4 x^{3}}{6}$

Step 3.3

Cancel the common factor of $4$ and $6$ .

Tap for more steps...

Step 3.3.1

Factor $2$ out of $4 x^{3}$ .

$\frac{2 (2 x^{3})}{6}$

Step 3.3.2

Cancel the common factors.

Tap for more steps...

Step 3.3.2.1

Factor $2$ out of $6$ .

$\frac{2 (2 x^{3})}{2 (3)}$

Step 3.3.2.2

Cancel the common factor.

$\frac{2 (2 x^{3})}{2 \cdot 3}$

Step 3.3.2.3

Rewrite the expression.

$\frac{2 x^{3}}{3}$