Calculus Examples

$f (x) = \frac{1}{2 t} + 1$

Step 1

Consider the difference quotient formula.

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

Step 2

Find the components of the definition.

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Step 2.1

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

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Step 2.1.1

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

$f (x + h) = \frac{1}{2 t} + 1$

Step 2.1.2

The final answer is $\frac{1}{2 t} + 1$ .

$\frac{1}{2 t} + 1$

Step 2.2

Find the components of the definition.

$f (x + h) = \frac{1}{2 t} + 1$

$f (x) = \frac{1}{2 t} + 1$

$f (x + h) = \frac{1}{2 t} + 1$

$f (x) = \frac{1}{2 t} + 1$

Step 3

Plug in the components.

$\frac{f (x + h) - f (x)}{h} = \frac{\frac{1}{2 t} + 1 - (\frac{1}{2 t} + 1)}{h}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Apply the distributive property.

$\frac{\frac{1}{2 t} + 1 - \frac{1}{2 t} - 1 \cdot 1}{h}$

Step 4.1.2

Multiply $- 1$ by $1$ .

$\frac{\frac{1}{2 t} + 1 - \frac{1}{2 t} - 1}{h}$

Step 4.1.3

Subtract $\frac{1}{2 t}$ from $\frac{1}{2 t}$ .

$\frac{0 + 1 - 1}{h}$

Step 4.1.4

Add $0$ and $1$ .

$\frac{1 - 1}{h}$

Step 4.1.5

Subtract $1$ from $1$ .

$\frac{0}{h}$

Step 4.2

Divide $0$ by $h$ .

$0$

Step 5