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:
$\displaystyle y=\frac{e^u - e^{-u}}{e^u + e^{-u}}=1-\frac{2e^{-u}}{e^u+e^{-u}}=1-\frac{2}{e^{2u}+1}$ , 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...