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

Let U(x,y) =e^(x) sin y , where x=st^(2), y =s^(2) t, s, t in R . Find (del U)/(del S), (del U)/(del t) and evaluate them at s=t=1.

Let z(x,y) =x^(3) - 3x^(2)y^(3) , where x = se^(t), y =se^(-t), s, t in R . Find (del z)/(del s) and (del z)/(del t)

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

Let z=e^(xy^(2)),x=t cos t,y=t sint . Find (dz)/(dt) at t=pi/2

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