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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- Nov 2nd 2010, 07:44 PMDannyMathHave 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! - Nov 2nd 2010, 08:07 PMtonio

Be sure you understand the following algebraic simplifications:

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

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