# Calculus Examples

Step 1

Step 1.1

To apply the Chain Rule, set as .

Step 1.2

Differentiate using the Power Rule which states that is where .

Step 1.3

Replace all occurrences of with .

Step 2

Step 2.1

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

Step 2.2

Differentiate using the Power Rule which states that is where .

Step 2.3

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

Step 2.4

Differentiate using the Power Rule which states that is where .

Step 2.5

Multiply by .

Step 3

Step 3.1

Apply the distributive property.

Step 3.2

Multiply by .

Step 3.3

Expand using the FOIL Method.

Step 3.3.1

Apply the distributive property.

Step 3.3.2

Apply the distributive property.

Step 3.3.3

Apply the distributive property.

Step 3.4

Simplify and combine like terms.

Step 3.4.1

Simplify each term.

Step 3.4.1.1

Rewrite using the commutative property of multiplication.

Step 3.4.1.2

Multiply by by adding the exponents.

Step 3.4.1.2.1

Move .

Step 3.4.1.2.2

Use the power rule to combine exponents.

Step 3.4.1.2.3

Add and .

Step 3.4.1.3

Multiply by .

Step 3.4.1.4

Multiply by .

Step 3.4.1.5

Rewrite using the commutative property of multiplication.

Step 3.4.1.6

Multiply by by adding the exponents.

Step 3.4.1.6.1

Move .

Step 3.4.1.6.2

Multiply by .

Step 3.4.1.6.2.1

Raise to the power of .

Step 3.4.1.6.2.2

Use the power rule to combine exponents.

Step 3.4.1.6.3

Add and .

Step 3.4.1.7

Multiply by .

Step 3.4.1.8

Multiply by .

Step 3.4.2

Subtract from .