If #f(x) =x-xe^(2x+4) # and #g(x) = cos9x #, what is #f'(g(x)) #?

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Answer 1 · 2018-01-02T08:03:19

#9sin9x(2cos9xe^(2cos9x+4)+e^(2cos9x+4)-1)#

Since #color(red)g(x)=color(red)(cos9x)#,

then

#f(color(red)g(x))=f(color(red)(cos9x))=color(red)(cos9x)-color(red)(cos9x)*e^(2color(red)(cos9x)+4)#

Let's differentiate it as a chained function and get:

#f'(g(x))=-sin9x*9-(-sin9x*9*e^(2cos9x+4)+cos9x*e^(2cos9x+4)* 2* (-sin9x*9))#

#=-9sin9x+9sin9xe^(2cos9x+4)+18sin9xcos9xe^(2cos9x+4)#

#=9sin9x(2cos9xe^(2cos9x+4)+e^(2cos9x+4)-1)#