1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Differentiable functions

  1. Nov 29, 2007 #1
    1. The problem statement, all variables and given/known data
    If f is differentiable at x=0 and g(x) = [f(x)]^2, f(0) = f'(0) = -1, then g'(0) =

    2. Relevant equations
    MC Answers:
    (A) -2 (B) -1 (C) 1 (D) 4 (E) 2

    3. The attempt at a solution

    The only thing I could think of was that if g(x) = (f(x))^2 then g'(0) = (f'(0))^2 and then g'(0) = 1. Does this make sense? I kind of feel like my logic is pseudo math and is giving me an incorrect answer.
  2. jcsd
  3. Nov 29, 2007 #2


    User Avatar
    Homework Helper

    I would say C) but I can't say if my thinking is correct...it amounts to the same as yours...except for one part
  4. Nov 29, 2007 #3


    User Avatar
    Science Advisor

    By the chain rule, g'(x) = 2f(x)f'(x).
  5. Nov 30, 2007 #4


    User Avatar
    Science Advisor

    You are right- your logic is pseudo math! :smile:The difficulty is that g'(x) is NOT (f'(x))2. As Avodyne said, you need to use the chain rule: g(x)= u2 and u= f(x). dg/dx= (dg/du)(du/dx).
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook