If #f(x)= - e^(5x # and #g(x) = 3 x #, how do you differentiate #f(g(x)) # using the chain rule?

1 Answer
Sep 30, 2016

Answer:

#f'(g(x))=-15e^(15x)#

Explanation:

To obtain f(g(x)) substitute g(x) in for x in f(x).

#rArrf(g(x))=f(color(red)(3x))=-e^(5(color(red)(3x))=-e^(15x)#

differentiate using the #color(blue)"chain rule"#

#color(orange)"Reminder " color(red)(bar(ul(|color(white)(a/a)color(black)(d/dx(e^x)=e^x)color(white)(a/a)|)))#

#f'(g(x))=-e^(15x).d/dx(15x)=-15e^(15x)#