Precalculus Examples

$f (x) = - 5 {(3)}^{x}$

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.

$f (x + h) = - 5 {(3)}^{x + h}$

Step 2.1.2

Simplify the result.

Tap for more steps...

Step 2.1.2.1

Remove parentheses.

$f (x + h) = - 5 \cdot 3^{x + h}$

Step 2.1.2.2

The final answer is $- 5 \cdot 3^{x + h}$ .

$- 5 \cdot 3^{x + h}$

Step 2.2

Find the components of the definition.

$f (x + h) = - 5 \cdot 3^{x + h}$

$f (x) = - 5 \cdot 3^{x}$

$f (x + h) = - 5 \cdot 3^{x + h}$

$f (x) = - 5 \cdot 3^{x}$

Step 3

Plug in the components.

$\frac{f (x + h) - f (x)}{h} = \frac{- 5 \cdot 3^{x + h} - (- 5 \cdot 3^{x})}{h}$

Step 4

Simplify.

Tap for more steps...

Step 4.1

Simplify the numerator.

Tap for more steps...

Step 4.1.1

Multiply $- 5$ by $- 1$ .

$\frac{- 5 \cdot 3^{x + h} + 5 \cdot 3^{x}}{h}$

Step 4.1.2

Factor $5$ out of $- 5 \cdot 3^{x + h} + 5 \cdot 3^{x}$ .

Tap for more steps...

Step 4.1.2.1

Factor $5$ out of $- 5 \cdot 3^{x + h}$ .

$\frac{5 (- 3^{x + h}) + 5 \cdot 3^{x}}{h}$

Step 4.1.2.2

Factor $5$ out of $5 \cdot 3^{x}$ .

$\frac{5 (- 3^{x + h}) + 5 (3^{x})}{h}$

Step 4.1.2.3

Factor $5$ out of $5 (- 3^{x + h}) + 5 (3^{x})$ .

$\frac{5 (- 3^{x + h} + 3^{x})}{h}$

Step 4.2

Simplify with factoring out.

Tap for more steps...

Step 4.2.1

Factor $- 1$ out of $3^{x}$ .

$\frac{5 (- 3^{x + h} - 1 (- 3^{x}))}{h}$

Step 4.2.2

Factor $- 1$ out of $- 3^{x + h} - 1 (- 3^{x})$ .

$\frac{5 (- (3^{x + h} - 3^{x}))}{h}$

Step 4.2.3

Simplify the expression.

Tap for more steps...

Step 4.2.3.1

Rewrite $- (3^{x + h} - 3^{x})$ as $- 1 (3^{x + h} - 3^{x})$ .

$\frac{5 (- 1 (3^{x + h} - 3^{x}))}{h}$

Step 4.2.3.2

Move the negative in front of the fraction.

$- \frac{5 (3^{x + h} - 3^{x})}{h}$

Step 5