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Math Help - Hard problem on the chain rule for multivariable function ??

  1. #1
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    Hard problem on the chain rule for multivariable function ??

    Hi ..
    this is a problem from old exam ..
    am lost .. i cant do anything!
    i know the chain rule for F(x,y) where x=g(s,t) and y = h(s,t)
    or for f(x,y,z,...) and x=g(s,t,...) y = h(s,t,....) and z=m(s,t,....) .. etc
    what am gonna to said as am good !
    but am lost at this

    Problem :
    Let F(s,t) be a differentiable function, let G(x,y) = F(x+y,xy),
    calculate G_x(2,3) and G_y(2,3) if F_s(2,3)=1, F_s(5,6)=1
    and F_t(2,3) = 4 and F_t(5,6) = 7

    G_x = differentiating G with respect to x
    F_t = differentiating F with respect to t
    and so on..
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  2. #2
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    Quote Originally Posted by TWiX View Post
    Hi ..
    this is a problem from old exam ..
    am lost .. i cant do anything!
    i know the chain rule for F(x,y) where x=g(s,t) and y = h(s,t)
    or for f(x,y,z,...) and x=g(s,t,...) y = h(s,t,....) and z=m(s,t,....) .. etc
    what am gonna to said as am good !
    but am lost at this

    Problem :
    Let F(s,t) be a differentiable function, let G(x,y) = F(x+y,xy),
    calculate G_x(2,3) and G_y(2,3) if F_s(2,3)=1, F_s(5,6)=1
    and F_t(2,3) = 4 and F_t(5,6) = 7

    G_x = differentiating G with respect to x
    F_t = differentiating F with respect to t
    and so on..
    Let s = x+y and t = xy

    By the chain rule

    G_x = F_s s_x + F_t t_x = F_s + y F_t<br />

    then let x = 2 and y = 3. Similarly for  G_y .
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