Results 1 to 2 of 2

Math Help - Using the Chain Rule to solve? Also, find the derivative?

  1. #1
    Newbie
    Joined
    Mar 2009
    Posts
    2

    Using the Chain Rule to solve? Also, find the derivative?

    I am confused on what to do with the chain rule. I have a problem that goes a bit like this:

    Assume that x, y, and z are all functions of time, t. Use the chain rule to find dz/dt, in terms of x, y, dx/dt and dy/dt if z= sin(x y).

    How do I use the chain rule to solve this? Please help me solve and tell me the steps you used to get to it. I have this so far: dz/dt = cosx dy/dt y dx/dt, but I'm pretty sure that's wrong.

    Also, I'm confused on how to find the derivative for this one. I get kind of confused when there are squares along with it:

    d/dx [sin(x^2)+cos^2(x)].

    Any help GREATLY appreciated! Thanks so much.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member Pinkk's Avatar
    Joined
    Mar 2009
    From
    Uptown Manhattan, NY, USA
    Posts
    419
    Chain rule (version 1)

    If z=f(x,y) and x=x(t),y=y(t) then we can have the following:

    \frac{dz}{dt}=\frac{\partial f}{\partial x}\frac{dx}{dt}+\frac{\partial f}{\partial y}\frac{dy}{dt}

    \frac{\partial f}{\partial x}=ycos(xy)
    \frac{\partial f}{\partial y}=xcos(xy)

    Since we are not given what x(t),y(t) are equal to in terms of t, we write the following

    \frac{dz}{dt}=ycos(xy)\frac{dx}{dt}+xcos(xy)\frac{  dy}{dt}


    For the second problem:

    \frac{d}{dx}(sin(x^{2})+cos^{2}x)=2xcos(x^{2})-2cosxsinx.

    Remember, \frac{d}{dx}f(g(x))=f'(g(x))g'(x)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] find derivative of a trig function (chain rule included)
    Posted in the Calculus Forum
    Replies: 10
    Last Post: May 8th 2011, 05:20 PM
  2. Replies: 10
    Last Post: November 21st 2010, 08:55 AM
  3. [SOLVED] Partial derivative using chain rule. Can't find my mistake.
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 19th 2010, 03:31 AM
  4. Replies: 3
    Last Post: June 7th 2010, 10:01 PM
  5. Replies: 5
    Last Post: October 19th 2009, 01:04 PM

Search Tags


/mathhelpforum @mathhelpforum