Differentiate and simplify!!! Please help?

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1 Answer
Feb 7, 2018

(a) #(df)/(dx)=1/(1+cosx)#
(b) #(df)/(dx)=(e^x(x-1))/(x+e^x)^2#

Explanation:

We use quotient formula here.

(a) As #f(x)=sinx/(1+cosx)#

#(df)/(dx)=(cosx(1+cosx)-sinx(-sinx))/(1+cosx)^2#

= #(cosx+cos^2x+sin^2x)/(1+cosx)^2#

= #(1+cosx)/(1+cosx)^2#

= #1/(1+cosx)#

(b) #f(x)=e^x/(x+e^x)#

#(df)/(dx)=(e^x(x+e^x)-e^x(1+e^x))/(x+e^x)^2#

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

= #(e^x(x-1))/(x+e^x)^2#