# Calculus Examples

,
Step 1
Write as an equation.
Step 2
To find elasticity of demand, use the formula .
Step 3
Substitute for in and simplify to find .
Substitute for .
Multiply by .
Subtract from .
Step 4
Find by differentiating the demand function.
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 into the formula for elasticity and simplify.
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.