Precalculus Examples

$y = e^{x}$

Step 1

Write $y = e^{x}$ as a function.

$f (x) = e^{x}$

Step 2

Consider the difference quotient formula.

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

Step 3

Find the components of the definition.

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Step 3.1

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

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Step 3.1.1

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

$f (x + h) = e^{x + h}$

Step 3.1.2

The final answer is $e^{x + h}$ .

$e^{x + h}$

Step 3.2

Find the components of the definition.

$f (x + h) = e^{x + h}$

$f (x) = e^{x}$

$f (x + h) = e^{x + h}$

$f (x) = e^{x}$

Step 4

Plug in the components.

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

Step 5

Multiply $- 1$ by $e^{x}$ .

$\frac{e^{x + h} - e^{x}}{h}$

Step 6