# Calculus Examples

Step 1

Differentiate both sides of the equation.

Step 2

The derivative of with respect to is .

Step 3

Step 3.1

Differentiate.

Step 3.1.1

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

Step 3.1.2

Differentiate using the Power Rule which states that is where .

Step 3.2

Evaluate .

Step 3.2.1

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

Step 3.2.2

Differentiate using the Power Rule which states that is where .

Step 3.2.3

Multiply by .

Step 3.3

Reorder terms.

Step 4

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

Step 5

Replace with .

Step 6

Step 6.1

Subtract from both sides of the equation.

Step 6.2

Divide each term in by and simplify.

Step 6.2.1

Divide each term in by .

Step 6.2.2

Simplify the left side.

Step 6.2.2.1

Cancel the common factor of .

Step 6.2.2.1.1

Cancel the common factor.

Step 6.2.2.1.2

Divide by .

Step 6.2.3

Simplify the right side.

Step 6.2.3.1

Move the negative in front of the fraction.

Step 7

Step 7.1

Remove parentheses.

Step 7.2

Remove parentheses.

Step 7.3

Simplify .

Step 7.3.1

Simplify each term.

Step 7.3.1.1

Use the power rule to distribute the exponent.

Step 7.3.1.1.1

Apply the product rule to .

Step 7.3.1.1.2

Apply the product rule to .

Step 7.3.1.2

Raise to the power of .

Step 7.3.1.3

Multiply by .

Step 7.3.1.4

One to any power is one.

Step 7.3.1.5

Raise to the power of .

Step 7.3.1.6

Cancel the common factor of .

Step 7.3.1.6.1

Factor out of .

Step 7.3.1.6.2

Cancel the common factor.

Step 7.3.1.6.3

Rewrite the expression.

Step 7.3.2

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

Step 7.3.3

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

Step 7.3.3.1

Multiply by .

Step 7.3.3.2

Multiply by .

Step 7.3.4

Combine the numerators over the common denominator.

Step 7.3.5

Add and .

Step 7.3.6

Move the negative in front of the fraction.

Step 8

Find the points where .

Step 9