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Math Help - Simple differentiation!

  1. #1
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    Simple differentiation!

    I am very out of practice with differentiation as I have not done it for over three years. However, I have just come across this problem and I need to solve it as soon as possible. I have tried reading around about how to do it, but to no avail.

    Get dx/dy when

    x = ay[1-((y/b)^3)]

    Please help!
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  2. #2
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    This may even be A-Level actually.

    Anyway I just used the product rule to break it down into two parts

    u=ay v=[1-((y/b)^3)]

    differentiating u is easy, but now I am struggling differentiating v. help?
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  3. #3
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    v = 1 - {\frac{y}{ b} }^{ 3}   dv = -3{\frac{y}{ b}}^{ 2}
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  4. #4
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    Can you just explain how you have done that please?
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  5. #5
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    Quote Originally Posted by ishida View Post
    Can you just explain how you have done that please?
    If it is with respect to y (which i have assumed), all you do is times the y term by the power, then reduce the power by 1.
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  6. #6
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    Is v = 1 - {\frac{y}{ b} }^{ 3}   or is v = 1 - {(\frac{y}{ b}) }^{ 3}   ??
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  7. #7
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    Ok, makes sense. However, in the solution I have been given there appears to be another term at the end. 1/b. Where has this come from?
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  8. #8
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    Quote Originally Posted by adam_leeds View Post
    Is v = 1 - {\frac{y}{ b} }^{ 3}   or is v = 1 - {(\frac{y}{ b}) }^{ 3}   ??
    The second of those.
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  9. #9
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    v = 1 - {(\frac{y}{ b}) }^{ 3}   You times just the right hand side by the power and the differntation of the brackets with respect to y which is 1/b then reduce the power by 1. It's called the chain rule
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  10. #10
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    Makes sense. Brilliant. Thank you for your help
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