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

Let U(x,y,z) = xyz, x=e^(-t), y=e^(-t) cos t, z= sin t, t in R . Find (dU)/(dt) .

If u(x,y,z) =xy^(2)z^(3), x= sin t, y = cos t, z=1 + e^(2t) , find (du)/(dx) .

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.

x=e^t (sin t + cos t ),y=e^t(sin t -cos t)

If x= e^t (sin t - cos t) , y= e^t (sin t + cos t) , find dy/dx at t= pi/4