Expert: Paul Klarreich - 5/20/2007

Question
let f(x)=g(h(x)), where h(2)=3,h'(2)=4, g(3)=2, and g"(3)=5. find f'(2)

Answer
Questioner:   bhavika
Category:  Calculus
 
Subject:  calculus
Question:  let f(x)=g(h(x)), where h(2)=3,h'(2)=4, g(3)=2, and g"(3)=5. find f'(2)

>> I think you meant to write  g'(3) = 5,  not g".
 
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Hi, Bhavika,

This is the chain rule.  If you have:

f(x) = g(h(x))

then write:  u = h(x)

and you have:

f(x) = g(u), and  u = h(x).

And:

df   df du
-- = -- --
dx   du dx

Your statement  h'(2) = 4  means  du/dx = 4  when  x = 2
Your statement  g'(3) = 5  means  df/du = 5  when  u = 3.

So f'(2) = g'(3) h'(2) = (4)(5) = 20