Calculus Examples

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

Step 1

Since $\frac{2}{3}$ is constant with respect to $x$ , the derivative of $\frac{2}{3} x^{6}$ with respect to $x$ is $\frac{2}{3} \frac{d}{d x} [x^{6}]$ .

$\frac{2}{3} \frac{d}{d x} [x^{6}]$

Step 2

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 6$ .

$\frac{2}{3} (6 x^{5})$

Step 3

Simplify terms.

Tap for more steps...

Step 3.1

Combine $6$ and $\frac{2}{3}$ .

$\frac{6 \cdot 2}{3} x^{5}$

Step 3.2

Multiply $6$ by $2$ .

$\frac{12}{3} x^{5}$

Step 3.3

Combine $\frac{12}{3}$ and $x^{5}$ .

$\frac{12 x^{5}}{3}$

Step 3.4

Cancel the common factor of $12$ and $3$ .

Tap for more steps...

Step 3.4.1

Factor $3$ out of $12 x^{5}$ .

$\frac{3 (4 x^{5})}{3}$

Step 3.4.2

Cancel the common factors.

Tap for more steps...

Step 3.4.2.1

Factor $3$ out of $3$ .

$\frac{3 (4 x^{5})}{3 (1)}$

Step 3.4.2.2

Cancel the common factor.

$\frac{3 (4 x^{5})}{3 \cdot 1}$

Step 3.4.2.3

Rewrite the expression.

$\frac{4 x^{5}}{1}$

Step 3.4.2.4

Divide $4 x^{5}$ by $1$ .

$4 x^{5}$