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Math Help - Have I gotten to the correct answer?

  1. #1
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    Have I gotten to the correct answer?

    Hi guys, I'm doing chain rule problems to practice for exam:

    I've encountered: y = (e^u - e^-u)/(e^u + e^-u)

    I've gotten: dy/du = 4/(e^u + e^-u)^2

    Is this the correct simplified answer? Thanks for the look!
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  2. #2
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    Quote Originally Posted by DannyMath View Post
    Hi guys, I'm doing chain rule problems to practice for exam:

    I've encountered: y = (e^u - e^-u)/(e^u + e^-u)

    I've gotten: dy/du = 4/(e^u + e^-u)^2

    Is this the correct simplified answer? Thanks for the look!

    Be sure you understand the following algebraic simplifications:


    y=\frac{e^u - e^{-u}}{e^u + e^{-u}}=1-\frac{2e^{-u}}{e^u+e^{-u}}=1-\frac{2}{e^{2u}+1} , and deriving now this is much simpler:

    y'=\frac{4e^{2u}}{(e^{2u}+1)^2} . Check now that this is just what you got...
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