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A few questions on a HUGE derivatives assignment

  1. Nov 27, 2011 #1
    Hi physics forums, this post may seem like it has lots of questions, but don't think that you are doing ''my homework for me,'' it's actually a huge assignment, in which im only going to ask a few questions about.

    this question is actualy easy (or seems to be), but i keep getting 64/3 and noon of the multiple choice answers

    the slope of the line tangent to the curve y3+(xy-1)2=0 at the point
    -9/4, -4 is:

    A.0 B.1/3 C.32/59 D.8/3 E.16/3

    I started by doing implicit differentiation getting

    then solved for dy/dx=(2y-2xy2)/(3y2+2x2y-2x)

    then i just plugged in the numbers and got 64/3, any idea on what's wrong?

    now this one:
    let f be the function give by ef(x)=3x+1, g be the function given by 2lng(x)=4x2-6 and h be the function given by h(x)=f(g(x)). Find h'(x)

    i rewrote both f and g the following way:

    i insert g into f, but don't know how exactly would it lead be to one of the following options:


    BTW, sorry if that was way too resumed up, it's just because of the hurry, hope that's enough


    EDIT: there is yet another question

    suppose that the function f has a continous second derivative for all x, and that f(0)=2, f'(0)=-3 and f''(0)=0. Let g be a function whose derivative is given by g'(x)=e-2x(3f(x)+2f'(x)) for all x

    a)write an equation of the line tangent to the graph of f at the point where x=0
    b) given that g(0)=4, write an equation of the line tangent to the graph of g at the point where x=0
    c)show that g''(x)=e-2x(-6f(x)-f'(x)+2f''(x))

    WOAH, that question completely blows my mind.

    I guess the equation for a) would be y=-3x+2
    for b), it would be just plugging in numbers

    in c) im completely lost
    Last edited: Nov 27, 2011
  2. jcsd
  3. Nov 27, 2011 #2


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    Homework Helper

    On the first one I think you got dy/dx right. You seem to have subbed the numbers wrong.
  4. Nov 28, 2011 #3


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    Science Advisor

    You might find it better to put x= -9/4, y= 4 here and then solve for dy/dx.

    Don't. Instead, use the chain rule: h'(x)= f'(g(x))g'(x)

    NEVER use the word "guess"- even when you do! Yes, that is correct.

    Yes. Make it so!

    You are given that [itex]g'(x)= e^{-3x(3f(x)- 2f'(x))}[/itex]

    Differentiate it!
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