Differentiate using the Product Rule which states that is where and .

Rewrite as .

Apply the distributive property.

Apply the distributive property.

Apply the distributive property.

Simplify each term.

Multiply by .

Rewrite using the commutative property of multiplication.

Rewrite using the commutative property of multiplication.

Multiply by by adding the exponents.

Use the power rule to combine exponents.

Add and .

Multiply by .

Subtract from .

Move .

Subtract from .

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

Differentiate using the Power Rule which states that is where .

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 .

Add and .

Reorder terms.

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

Apply the distributive property.

Combine terms.

Multiply by by adding the exponents.

Move .

Use the power rule to combine exponents.

Add and .

Move to the left of .

Move to the left of .

Multiply by .

Add and .

Find the Derivative Using Product Rule – d/da x^4(a-2x^3)^2