# Calculus Examples

Rewrite as .

Expand using the FOIL Method.

Apply the distributive property.

Apply the distributive property.

Apply the distributive property.

Remove parentheses.

Simplify and combine like terms.

Simplify each term.

Use the power rule to combine exponents.

Add and to get .

Remove parentheses around .

Move to the left of the expression .

Multiply by to get .

Rewrite as .

Move .

Use the power rule to combine exponents.

Add and to get .

Simplify .

Multiply by to get .

Multiply by to get .

Subtract from to get .

Move .

Subtract from to get .

Differentiate both sides of the equation.

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 Product Rule which states that is where and .

Rewrite as .

Differentiate using the Power Rule which states that is where .

Multiply by to get .

Evaluate .

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 .

Simplify.

Apply the distributive property.

Remove parentheses around .

Remove parentheses.

Reorder terms.

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

Differentiate using the Power Rule which states that is where .

Rewrite as .

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

Add and to get .

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

Since contains the variable to solve for, move it to the left side of the equation by subtracting from both sides.

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

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

Reorder and .

Reorder and .

Reorder and .

Factor out of .

Factor out of .

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.

Simplify terms.

Combine the numerators over the common denominator.

Simplify each term.

Simplify the numerator.

Factor out of .

Multiply by to get .

Combine the numerators over the common denominator.

Simplify the numerator.

Apply the distributive property.

Multiply by to get .

Simplify terms.

Factor out of .

Rewrite as .

Move .

Multiply by to get .

Factor out of .

Rewrite as .

Move .

Multiply by to get .

Factor out of .

Rewrite as .

Factor out of .

Rewrite as .

Factor out of .

Rewrite as .

Move .

Multiply by to get .

Factor out of .

Rewrite as .

Move .

Multiply by to get .

Factor out of .

Rewrite as .

Factor out of .

Rewrite as .

Cancel the common factor.

Rewrite the expression.

Replace with .