# Calculus Examples

Step 1

Step 1.1

Use to rewrite as .

Step 1.2

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

Step 2

Step 2.1

To apply the Chain Rule, set as .

Step 2.2

Differentiate using the Power Rule which states that is where .

Step 2.3

Replace all occurrences of with .

Step 3

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

Step 4

Combine and .

Step 5

Combine the numerators over the common denominator.

Step 6

Step 6.1

Multiply by .

Step 6.2

Subtract from .

Step 7

Step 7.1

Move the negative in front of the fraction.

Step 7.2

Combine and .

Step 7.3

Move to the denominator using the negative exponent rule .

Step 7.4

Combine and .

Step 7.5

Cancel the common factor.

Step 7.6

Rewrite the expression.

Step 8

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

Step 9

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

Step 10

Differentiate using the Power Rule which states that is where .

Step 11

Multiply by .

Step 12

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

Step 13

Step 13.1

Add and .

Step 13.2

Combine and .