# Calculus Examples

Differentiate both sides of the equation.

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 .

Multiply by .

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 .

Remove parentheses around .

Move to the left of the expression .

Multiply by .

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 .

Simplify.

Remove parentheses.

Add and .

Reorder terms.

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

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

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.

Subtract from both sides of the equation.

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 .

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 .

Combine the numerators over the common denominator.

Simplify the numerator.

Apply the distributive property.

Move .

Simplify .

Remove parentheses around .

Simplify each term.

Multiply by .

Simplify with factoring out.

Factor out of .

Factor out of .

Rewrite as .

Move .

Multiply by .

Factor out of .

Factor out of .

Rewrite as .

Move .

Multiply by .

Factor out of .

Simplify the expression.

Rewrite as .

Reorder terms.

Move the negative in front of the fraction.

Divide each term by and simplify.

Divide each term in by .

Simplify the left side of the by cancelling the common factors.

Reduce the expression by cancelling the common factors.

Cancel the common factor.

Rewrite the expression.

Reduce the expression by cancelling the common factors.

Cancel the common factor.

Divide by .

Simplify the right side of the equation.

Multiply the numerator by the reciprocal of the denominator.

Multiply and .

Simplify the expression.

Remove parentheses around .

Reorder factors in .

Replace with .