# Calculus Examples

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 .
Since is constant with respect to , the derivative of with respect to is .
Set the derivative equal to then solve for .
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 .
Simplify the right side of the equation.
Divide by .
Multiply by .
After finding the point that makes the derivative equal to or undefined, the interval to check where is increasing and where it is decreasing is .
Substitute a value from the interval into the derivative to determine if the function is increasing or decreasing.
Replace the variable with in the expression.
Simplify the result.
Multiply by .
At the derivative is . Since this is negative, the function is decreasing on .
Decreasing on since
Decreasing on since
Substitute a value from the interval into the derivative to determine if the function is increasing or decreasing.
Replace the variable with in the expression.
Simplify the result.
Multiply by .