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

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

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