Question

高数.求 y=ch^2（x-1/x+1）的导数

Answer 1

你好!

令u=(x-1)/(x+1)

v=ch u = [e^u +e^(-u)] /2

y=v^2

u'=[(x+1)-(x-1)] / (x+1)^2 = 2/(x+1)^2

v'=[e^u -e^(-u)] /2 *u' = (sh u)*u'

y'=2v*v'

∴y'= [e^u +e^(-u)] * [e^u -e^(-u)] /2 * 2/(x+1)^2

=[e^(2u) -e^(-2u) ] /(x+1)^2

= sh(2u) /(x+1)^2

= sh[2(x-1)/(x+1)] /(x+1)^2