Calculus Examples

$f (x) = x^{\frac{1}{3}}$

Step 1

Consider the difference quotient formula.

$\frac{f (x + h) - f (x)}{h}$

Step 2

Find the components of the definition.

Tap for more steps...

Step 2.1

Evaluate the function at $x = x + h$ .

Tap for more steps...

Step 2.1.1

Replace the variable $x$ with $x + h$ in the expression.

$f (x + h) = {(x + h)}^{\frac{1}{3}}$

Step 2.1.2

The final answer is ${(x + h)}^{\frac{1}{3}}$ .

${(x + h)}^{\frac{1}{3}}$

Step 2.2

Find the components of the definition.

$f (x + h) = {(x + h)}^{\frac{1}{3}}$

$f (x) = x^{\frac{1}{3}}$

$f (x + h) = {(x + h)}^{\frac{1}{3}}$

$f (x) = x^{\frac{1}{3}}$

Step 3

Plug in the components.

$\frac{f (x + h) - f (x)}{h} = \frac{{(x + h)}^{\frac{1}{3}} - (x^{\frac{1}{3}})}{h}$

Step 4

Multiply $- 1$ by $x^{\frac{1}{3}}$ .

$\frac{{(x + h)}^{\frac{1}{3}} - x^{\frac{1}{3}}}{h}$

Step 5