How do you differentiate # y = 2/[(e^(x) + e^(-x)]#?

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Answer 1 · 2017-10-17T10:51:50

#(dy)/(dx)=-(2(e^x-e^(-x)))/((e^x+e^(-x))^2#

we will use teh quotient rule

#y=u/v=>y'=(vu'-uv')/v^2#

#y=2/(e^x+e^(-x)#

#u=2=>u'=0#

#v=e^x+e^(-x)=>v'=e^x-e^(-x)#

#;.y'=(0-2(e^x-e^(-x)))/(e^x+e^(-x))^2#

#(dy)/(dx)=-(2(e^x-e^(-x)))/((e^x+e^(-x))^2#