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Math Help - Need help with a few derivatives

  1. #1
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    Need help with a few derivatives

    Hi,

    I'm given 3 functions I need to find f' of:

    f(x) = x(3x-9)^3

    f(x) = x√(2x+3)

    f(x) = t^2
    √(t-2)

    You're supposed to use the chain rule for these, but I run into a problem. For example, the second function. I start by changing the equation to x(2x+3)^1/2, I multiply x by the exponent (1/2), subtract 1 from the exponent, and then multiply by the derivative (2) to finish with x(2x+3)^-1/2. But that doesn't give the right answer. Actually, I managed to get every other problem on the assignment correct except for these ones that have a variable multiplied by a polynomial. Could anyone tell me what I've done wrong?

    Thanks!
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  2. #2
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    Re: Need help with a few derivatives

    So what you did was just treat the first "x" as a constant? That, of course, is wrong. Use the product rule.
    The derivative of x(3x- 9)^3 is (3x- 9)^2+x(3(3x- 9)^2(3)).

    Another way to do this is to move the "x" into the rest of the function: f(x)= x(3x- 9)^3= (x^{1/3}(3x- 9))^3= (3x^{4/3}- 9x^{1/3})^3.
    Last edited by HallsofIvy; November 9th 2013 at 02:09 PM.
    Thanks from KevinShaughnessy
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  3. #3
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    Re: Need help with a few derivatives

    Quote Originally Posted by KevinShaughnessy View Post
    Hi,
    I'm given 3 functions I need to find f' of:
    f(x) = x√(2x+3)
    x\sqrt{2x+3} is a product.

    Here is the back-of-the-book answer: \sqrt{2x+3}+\frac{x^2}{\sqrt{2x+3}}

    Can you explain why?
    Thanks from KevinShaughnessy
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  4. #4
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    Re: Need help with a few derivatives

    Awesome, I see where I went wrong now. Thanks a lot guys.
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