How do you differentiate # f(x)= (6e^(-x)+2)^3 # using the chain rule?

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Answer 1 · 2015-12-22T12:23:29

#f'(x)=-18e^-x(6e^-x+2)#

According to the chain rule:

#f'(x)=3(6e^-x+2)^2d/dx[6e^-x+2]#

Once again applying the chain rule:

#d/dx[6e^-x+2]=6e^-xd/dx[-x]#

#=>-6e^-x#

Thus,

#f'(x)=-18e^-x(6e^-x+2)#