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Math Help - Derivation

  1. #1
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    Derivation

    Can someone please help me derivate this

    h(x)=(x+1)^2(2x+1)^3













    Thank you!
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  2. #2
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    Quote Originally Posted by Coach View Post
    h(x)=(x+1)^2(2x+1)^3
    Semi-nice way: product rule. (Do you know what the product rule is?)

    Nasty way: expand the expression but this has a benefit, you'll only have to apply the power rule.
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  3. #3
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    Thank you for your reply!

    I do know the product rule in case you are talking about the uv´+vu´ rule, where the accent indicates derivated(I am sorry, I am very bad at these terms, since the textbook we are using is in Finnish). However, whenever I try to apply this rule, I get the wrong answer. Here is what I did.

    (X+1)^3*2(2X-1)^1+ (2X-1)^2*3(X+1)^2
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  4. #4
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    Yes, that states the product rule. (Don't worry about the terms, I'm chilean and I have to learn them anyway.)

    \Big[ {f(x) \cdot g(x)} \Big]' = f'(x) \cdot g(x) + f(x) \cdot g'(x).

    The function is h(x)=(x+1)^2(2x+1)^3,

    So h'(x)=2(x+1)\cdot(2x+1)^3+3(x+1)^2(2x+1)^2\cdot2.

    Can you take it from there?
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  5. #5
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    Yes. Thank you!


    But where did you get the last 2 from?
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  6. #6
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    It's the chain rule; the derivative of (2x+1)^3 is 3(2x+1)^2\cdot(2x+1)'. That's why appears the 2.
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