# Calculus Examples

Set as a function of .
Find the derivative.
By the Sum Rule, the derivative of with respect to is .
Differentiate using the Power Rule which states that is where .
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 to get .
Since is constant with respect to , the derivative of with respect to is .
Set the derivative equal to then solve the equation .
Subtract from both sides of the equation.
Divide each term by and simplify.
Divide each term in by .
Reduce the expression by cancelling the common factors.
Cancel the common factor.
Divide by to get .
Simplify the right side of the equation.
Divide by to get .
Multiply by to get .
Solve the original function at .
Replace the variable with in the expression.
Simplify the result.
Simplify each term.
Raise to the power of to get .
Multiply by to get .
Simplify by subtracting numbers.
Subtract from to get .
Subtract from to get .