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Math Help - Help - Partial Derivatives of f(x,y)

  1. #1
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    Exclamation Help - Partial Derivatives of f(x,y)

    Hi , can anyone help me with this problem please

    (a) Find w''(t) if w=x^2 y , x = e^-t ,  y=ln(t)

    i was able to do it for w'(t) easily

    w'(t) = dw/dx dx/dt + dw/dy dy/dt

    However i dont know how to do it for w''(t) in the same way as w'(t)


    (b) Find w''(t) if w=f(x,y) , x=e^t , y = 2t - 1


    w'(t) = df/dx dx/dt + df/dy dy/dt

    w''(t) = ?!?!?!?!?!


    Please i need a little bit of explanation on finding w''(t)

    Thanks
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  2. #2
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    Quote Originally Posted by x7amoooodx View Post
    Hi , can anyone help me with this problem please

    (a) Find w''(t) if w=x^2 y , x = e^-t , y=ln(t)

    i was able to do it for w'(t) easily

    w'(t) = dw/dx dx/dt + dw/dy dy/dt

    However i dont know how to do it for w''(t) in the same way as w'(t)
    w'(t)=2xy x'(t) + x^2 y'(t)

    w''(t)=\left[\frac{\partial}{\partial x} w'\right] x'+\left[\frac{\partial}{\partial y} w'\right] y'

    etc.

    CB
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