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

Differentiate using the Product Rule which states that is where and .
Rewrite as .
Expand using the FOIL Method.
Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify and combine like terms.
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.
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 .
Simplify the expression.
Reorder terms.
Since is constant with respect to , the derivative of with respect to is .
Simplify.
Apply the distributive property.
Combine terms.
Multiply by by adding the exponents.
Move .
Use the power rule to combine exponents.