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If u(x,y) =x^(2)y + 3xy^(4), x = e^(t) a...

If `u(x,y) =x^(2)y + 3xy^(4), x = e^(t)` and y= sin t, find `(du)/(dx)` and evaluate it at t=0.

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Knowledge Check

  • If g(x,y) = 3x^(2) - 5y + 2y^(2), x(t) =e^(t) and y(t) = cos t , then (dg)/(dt) is equal to

    A
    `6e^(2t) + 5 sin t - 4 cos t sin t`
    B
    `6e^(2t) - 5 sin t + 4 cos t sin t`
    C
    `3e^(2t) + 5 sin t + 4 cos t sin t`
    D
    `3e^(2t) - 5 sin t + 4 cos t sin t`

  • If g(x, y) = 3x^(2) - 5y + 2y^(2), x(t) = e^(t) and y(t) = cos t , then (dg)/(d t) is equal to

    A
    `6e^(2t) + 5 sin t - 4 cos t sin t`
    B
    `6e^(2t) - 5 sin t + 4 cos t sin t`
    C
    `3e^(2t) + 5 sin t + 4 cos t sin t`
    D
    `3e^(2t) - 5 sin t + 4 cos t sin t`

    • Similar Questions

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    If w(x,y,z) =x^(2) + y^(2)+ z^(2), x=e^(t), y=e^(t) sin t and z=e^(t) cos t , find (dw)/(dt) .

    If f (x,y) =x ^(2) + xy+y ^(2),x =t ,y=t ^(2) then (df )/(dt)=

    Let g (x,y)=x^2-yx + sin (x+y), x (t) = e^(3t) , y(t) = t^2, t in R. Find (dg)/(dt) .

    If z(x,y) =x tan^(-1)(xy), x=t^(2), y=se^(t), s, t in R , Find (del z)/(del s) and (del z)/(del t) at s=t=1.

    If z(x,y) = x tan^(-1) (x,y) , x = t ^2, y = se^t, s t in R . Find (delz)/(delt) at s = t = 1 .

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