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
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)#
