Calculus Examples
,
Step 1
To find elasticity of demand, use the formula .
Step 2
Step 2.1
Substitute for .
Step 2.2
Simplify each term.
Step 2.2.1
Raise to the power of .
Step 2.2.2
Multiply by .
Step 2.3
Subtract from .
Step 3
Step 3.1
Differentiate the demand function.
Step 3.2
Differentiate.
Step 3.2.1
By the Sum Rule, the derivative of with respect to is .
Step 3.2.2
Since is constant with respect to , the derivative of with respect to is .
Step 3.3
Evaluate .
Step 3.3.1
Since is constant with respect to , the derivative of with respect to is .
Step 3.3.2
Differentiate using the Power Rule which states that is where .
Step 3.3.3
Multiply by .
Step 3.4
Subtract from .
Step 4
Step 4.1
Substitute for .
Step 4.2
Substitute the values of and .
Step 4.3
Cancel the common factor of and .
Step 4.3.1
Factor out of .
Step 4.3.2
Cancel the common factors.
Step 4.3.2.1
Factor out of .
Step 4.3.2.2
Cancel the common factor.
Step 4.3.2.3
Rewrite the expression.
Step 4.4
Multiply by .
Step 4.5
Cancel the common factor of .
Step 4.5.1
Factor out of .
Step 4.5.2
Cancel the common factor.
Step 4.5.3
Rewrite the expression.
Step 4.6
The absolute value is the distance between a number and zero. The distance between and is .
Step 5
Since , the demand is unitary.