# Calculus Examples

Find Where dy/dx is Equal to Zero
Differentiate both sides of the equation.
The derivative of with respect to is .
Differentiate the right side of the equation.
By the Sum Rule, the derivative of with respect to is .
Differentiate using the Power Rule which states that is where .
Since is constant with respect to , the derivative of with respect to is .
Reform the equation by setting the left side equal to the right side.
Replace with .
Set then solve for in terms of .
Rewrite the equation as .
Rewrite as a set of linear factors.
Divide each term by and simplify.
Divide each term in by .
Simplify the left side of the by cancelling the common factors.
Multiply by to get .
Reduce the expression by cancelling the common factors.
Cancel the common factor.
Divide by to get .
Divide by to get .
Take the cube root of both sides of the equation to eliminate the exponent on the left side.
Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
Solve for .
Simplify each term.
Remove parentheses around .
Raising to any positive power yields .