# Calculus Examples

Differentiate using the Power Rule which states that is where .
Set the derivative equal to .
Solve for .
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 .
Divide by .
Take the root of both sides of the to eliminate the exponent on the left side.
The complete solution is the result of both the positive and negative portions of the solution.
Simplify the right side of the equation.
Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
is equal to .
Substitute the values of which cause the derivative to be into the original function.
Raising to any positive power yields .
Find the domain of the derivative.
The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.
Interval Notation:
Set-Builder Notation:
Since there are no values of where the derivative is undefined, there are no additional critical points.