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

Let f :R ^(+) to R be a differentiable function with f (1)=3 and satisfying : int _(1) ^(xy) f(t) dt =y int_(1) ^(x) f (t) dt +x int_(1) ^(y) f (t) dt AA x, y in R^(+), then f (e) =

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

If y = int_(0)^(x) (t^(2))/(sqrt(t^(2)+1))dt then (dy)/(dx) at x=1 is