# Calculus Examples

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 to get .

Since is constant with respect to , the derivative of with respect to is .

Add and to get .

Since does not contain the variable to solve for, move it to the right side of the equation by adding to both sides.

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 to get .

Replace the variable with in the expression.

Simplify the result.

Simplify each term.

Apply the product rule to .

Raise to the power of to get .

Raise to the power of to get .

Simplify .

Write as a fraction with denominator .

Multiply and to get .

Multiply by to get .

Move the negative in front of the fraction.

To write as a fraction with a common denominator, multiply by .

Write each expression with a common denominator of , by multiplying each by an appropriate factor of .

Combine.

Multiply by to get .

Combine the numerators over the common denominator.

Multiply by to get .

Multiply by to get .

Subtract from to get .

Move the negative in front of the fraction.

To write as a fraction with a common denominator, multiply by .

Write each expression with a common denominator of , by multiplying each by an appropriate factor of .

Combine.

Multiply by to get .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by to get .

Multiply by to get .

Add and to get .

Move the negative in front of the fraction.

The final answer is .

The horizontal tangent lines on function are .