If f(x)= 1/x f(x)=1x and g(x) = 1/x g(x)=1x, how do you differentiate f'(g(x)) using the chain rule?

1 Answer
Yonas Yohannes
Mar 25, 2016

(df(g(x)))/(dx)=color(red)(-x^2)*color(blue)((-1/x^2)= 1

Explanation:

Given: f(x) = 1/x and g(x)=1/x
Required: (df(g(x)))/(dx)=f'(g(x))
Definition and Principles - Chain Rule:
(df(g(x)))/(dx)=color(red)((df(g))/(dg))*color(blue)((dg(x))/(dx))
color(red)((df(g))/(dg)) = -1/g^2 but g=1/x, thus
color(red)((df(g))/(dg)) = -1/(1/(x^2))=-x^2
color(blue)((dg(x))/(dx))=-1/x^2 thus
(df(g(x)))/(dx)=color(red)(-x^2)*color(blue)((-1/x^2)= 1

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