# Calculus Examples

Step 1
Set as a function of .
Step 2
Find the derivative.
Step 2.1
Since is constant with respect to , the derivative of with respect to is .
Step 2.2
Differentiate using the Power Rule which states that is where .
Step 2.3
Multiply by .
Step 3
Set the derivative equal to then solve the equation .
Step 3.1
Divide each term in by and simplify.
Step 3.1.1
Divide each term in by .
Step 3.1.2
Simplify the left side.
Step 3.1.2.1
Cancel the common factor of .
Step 3.1.2.1.1
Cancel the common factor.
Step 3.1.2.1.2
Divide by .
Step 3.1.3
Simplify the right side.
Step 3.1.3.1
Divide by .
Step 3.2
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 3.3
Simplify .
Step 3.3.1
Rewrite as .
Step 3.3.2
Pull terms out from under the radical, assuming positive real numbers.
Step 3.3.3
Plus or minus is .
Step 4
Solve the original function at .
Step 4.1
Replace the variable with in the expression.
Step 4.2
Simplify the result.
Step 4.2.1
Raising to any positive power yields .
Step 4.2.2
Multiply by .
Step 4.2.3