SOLUTION: Use the product rule to differentiate each of the following with respect to x. a) (1-x^2)^2(1+2x^2) b) x^2(1-4x)^3

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Question 1190933: Use the product rule to differentiate each of the following with respect to x.
a) (1-x^2)^2(1+2x^2)
b) x^2(1-4x)^3
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Use the product rule to differentiate each of the following with respect to x.
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a) (1-x^2)^2(1+2x^2)
= d/dx((1-x^2)^2 * (1+2x^2) + (1-x^2)^2 * d/dx(1+2x^2)
= 2%2A%281-x%5E2%29%2A%28-2x%29%2A%281%2B2x%5E2%29+%2B+%28%281-x%5E2%29%5E2%29%2A4x
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b) x^2(1-4x)^3
d/dx = 2x%2A%281-4x%29%5E3+%2B+%28x%5E2%29%2A3%281-4x%29%5E2%2A%28-4%29
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Some combining of terms is possible.