If #f(x) =xe^x# and #g(x) = sinx-x#, what is #f'(g(x)) #?

1 Answer
Lucy
Jul 11, 2018

#f'(g(x))=(cosx-1)e^(sinx-x)(sinx-x+1)#

Explanation:

#f(x)=xe^x#
#g(x)=sinx-x#

#f(g(x))# means that we sub #sinx-x# into any #x# in #f(x)#
#f(g(x))=(sinx-x)e^(sinx-x)#

#f'(g(x))=(sinx-x)times(cosx-1)e^(sinx-x)+e^(sinx-x)times (cosx-1)#

#f'(g(x))=(sinx-x)(cosx-1)e^(sinx-x)+(cosx-1)e^(sinx-x)#

#f'(g(x))=(cosx-1)e^(sinx-x)(sinx-x+1)#

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