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How do you find the derivative of the function #y=cos((1-e^(2x))/(1+e^(2x)))#?

1 Answer

May 27, 2018

#y'=4*e^(2*x)/(1+e^(2+x))^2*sin((1-e^(2x))/(1+e^(2*x)))#

Explanation:

Using the chain rule, then we get
#y'=-sin((1-e^(2x))/(1+e^(2x)))*(-2e^(2x)(1+e^(2x))-(1-e^(2x))*e^(2x))/(1+e^(2x))^2#

#y=-sin((1-e^(2x))/(1+e^(2x)))*(2e^(2x)(-1-e^(2x)-1+e^(2x))/(1+e^(2x))^2)#
#y'=4e^(2x)/(1+e^(2x))^2*sin((1-e^(2x))/(1+e^(2x)))#

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