Calculus Examples

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

Step 1

Simplify the numerator.

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Step 1.1

Factor $f$ out of $f (a + h) - f a$ .

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Step 1.1.1

Factor $f$ out of $- f a$ .

$\frac{f (a + h) + f (- 1 a)}{h}$

Step 1.1.2

Factor $f$ out of $f (a + h) + f (- 1 a)$ .

$\frac{f (a + h - 1 a)}{h}$

$\frac{f (a + h - 1 a)}{h}$

Step 1.2

Rewrite $- 1 a$ as $- a$ .

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

Step 1.3

Subtract $a$ from $a$ .

$\frac{f (h + 0)}{h}$

Step 1.4

Add $h$ and $0$ .

$\frac{f h}{h}$

$\frac{f h}{h}$

Step 2

Cancel the common factor of $h$ .

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Step 2.1

Cancel the common factor.

$\frac{f h}{h}$

Step 2.2

Divide $f$ by $1$ .

$f$

$f$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$