# Calculus Examples

Set as a function of .
Find the derivative.
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 .
Set the derivative equal to then solve the equation .
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Set the first factor equal to and solve.
Set the first factor equal to .
Rewrite the equation as .
Since , there are no solutions.
No solution
No solution
Set the next factor equal to and solve.
Set the next factor equal to .
Take the square root of both sides of the equation 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 .
Solve the original function at .
Replace the variable with in the expression.
Simplify the result.
Remove parentheses around .
Raising to any positive power yields .
Multiply by .