# Calculus Examples

,

Step 1

Write as an equation.

Step 2

To find elasticity of demand, use the formula .

Step 3

Substitute for .

Multiply by .

Subtract from .

Step 4

Differentiate the demand function.

Differentiate.

By the Sum Rule, the derivative of with respect to is .

Since is constant with respect to , the derivative of with respect to is .

Evaluate .

Since is constant with respect to , the derivative of with respect to is .

Differentiate using the Power Rule which states that is where .

Multiply by .

Subtract from .

Step 5

Substitute for .

Substitute the values of and .

Cancel the common factor of .

Factor out of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Combine and .

Multiply by .

Divide by .

The absolute value is the distance between a number and zero. The distance between and is .

Step 6

Since , the demand is elastic.