# Calculus Examples

Differentiate both sides of the equation.

The derivative of with respect to is .

By the Sum Rule, the derivative of with respect to is .

Evaluate .

Differentiate using the Product Rule which states that is where and .

Differentiate using the chain rule, which states that is where and .

To apply the Chain Rule, set as .

Differentiate using the Power Rule which states that is where .

Replace all occurrences of with .

Rewrite as .

Differentiate using the Power Rule which states that is where .

Remove parentheses around .

Remove parentheses around .

Move to the left of the expression .

Multiply by to get .

Remove parentheses around .

Move to the left of the expression .

Multiply by to get .

Evaluate .

Differentiate using the Product Rule which states that is where and .

Differentiate using the chain rule, which states that is where and .

To apply the Chain Rule, set as .

Differentiate using the Power Rule which states that is where .

Replace all occurrences of with .

Rewrite as .

Differentiate using the Power Rule which states that is where .

Remove parentheses around .

Remove parentheses around .

Move to the left of the expression .

Multiply by to get .

Remove parentheses around .

Move to the left of the expression .

Multiply by to get .

Simplify.

Remove parentheses.

Reorder terms.

Reform the equation by setting the left side equal to the right side.

Since is on the right side of the equation, switch the sides so it is on the left side of the equation.

Subtract from both sides of the equation.

Move all terms not containing to the right side of the equation.

Subtract from both sides of the equation.

Subtract from both sides of the equation.

Factor out of .

Reorder and .

Reorder and .

Reorder and .

Factor out of .

Factor out of .

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 .

Simplify the right side of the equation.

Combine the numerators over the common denominator.

Simplify the numerator.

Factor out of .

Combine exponents.

Simplify with factoring out.

Reorder terms.

Factor out of .

Rewrite as .

Move .

Multiply by to get .

Factor out of .

Rewrite as .

Move .

Multiply by to get .

Factor out of .

Simplify the expression.

Rewrite as .

Move the negative in front of the fraction.

Reorder factors in .

Replace with .