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# Calculus Examples

Step 1

Step 1.1

To apply the Chain Rule, set as .

Step 1.2

The derivative of with respect to is .

Step 1.3

Replace all occurrences of with .

Step 2

Step 2.1

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

Step 2.2

Multiply by .

Step 2.3

Differentiate using the Power Rule which states that is where .

Step 2.4

Multiply by .

Step 3

Step 3.1

Apply the product rule to .

Step 3.2

Apply the distributive property.

Step 3.3

Combine terms.

Step 3.3.1

Multiply by .

Step 3.3.2

Combine and .

Step 3.3.3

Cancel the common factor of and .

Step 3.3.3.1

Factor out of .

Step 3.3.3.2

Cancel the common factors.

Step 3.3.3.2.1

Factor out of .

Step 3.3.3.2.2

Cancel the common factor.

Step 3.3.3.2.3

Rewrite the expression.

Step 3.4

Simplify the denominator.

Step 3.4.1

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

Step 3.4.2

Combine the numerators over the common denominator.

Step 3.4.3

Multiply by .

Step 3.5

Multiply the numerator by the reciprocal of the denominator.

Step 3.6

Multiply by .