If `w = e ^(xy)` wh4ere `x = t ^(2), y = t ^(3)` show that `(dw)/(dt)=5t ^(4) e ^(t^(5)).`

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

If w=xy + z, where x=cos t, y = sin t, z=t, find (dw)/(dt) .

Find the vaoue of each of the folllowing polynomials for the indicated value of variables: (i) p(x) = 4x ^(2) - 3x + 7 at x =1 (ii) q (y) = 2y ^(3) - 4y + sqrt11 at y =1 (iii) r (t) = 4t ^(4) + 3t ^(3) -t ^(2) + 6 at t =p, t in R (iv) s (z) = z ^(3) -1 at z =1 (v) p (x) = 3x ^(2) + 5x -7 at x =1 (vii) q (z) = 5z ^(3) - 4z + sqrt2 at z =2

If w=x+2y+z^2and x= cos t , y = sin t, z = 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

If x=e^(cos2t) and y=e^(sin2t) , prove that (dy)/(dx)=-(ylogx)/(xlogy)