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Math Help - chain rule

  1. #1
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    chain rule

    find dy/dx

    y=xto3(5xto2 =1)to-2/3
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  2. #2
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    (5xto2 = 1) represents (5x^2 ? 1)
    What is the operation?
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  3. #3
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    ok the answer in the book is 1/3xto2(5xto2 +1)to-5/3 (25x + 9)

    I started the problem like this
    -3xto2(5xto2 +1)to-5/3 (10x)

    do am I on the right track?
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  4. #4
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    You need to use the product rule to compute the derivative.

    x^3(5x^2 + 1)^{-2/3}

    Let u = x^3 and v = (5x^2 + 1)^{-2/3}.

    Then the derivative of the function uv is:

    u \cdot \frac{dv}{dx} + v \cdot \frac{du}{dx}.

    Can you calculate \frac{du}{dx} and \frac{dv}{dx}?
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  5. #5
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    so it will be like this?

    (xto3)-2/3(10x)to-5/3 + (5xto2 +1)to-2/3(3xto2)
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  6. #6
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    Quote Originally Posted by homerb View Post
    so it will be like this?

    (xto3)-2/3(10x)to-5/3 + (5xto2 +1)to-2/3(3xto2)
    The right side of your equation is correct, but the left is not.
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  7. #7
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    that is where I have problems. can you show me how it is done
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