# Calculus Examples

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 .

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 .

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 .

Simplify.

Apply the distributive property.

Remove parentheses around .

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.

Factor out of .

Factor out of .

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 .

Multiply by to get .

Simplify with factoring out.

Factor out of .

Factor out of .

Factor out of .

Simplify the expression.

Rewrite as .

Move the negative in front of the fraction.

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.

Multiply the numerator by the reciprocal of the denominator.

Cancel the common factor of .

Factor out the greatest common factor .

Cancel the common factor.

Rewrite the expression.

Multiply and to get .

Replace with .