Consider the function z=f(x,y)=x2yexy. Let v=(3,4).(1) Find the gradient vector gradf(x,y).(2) Find the tangent plane to the surface z=f(x,y) when (x,y)=(0,1).(Hint: Recall that the tangent plane to the surface z=f(x,y) at (x0,y0,z0) has equation z-z0=fx'(x0,y0)(x-x0)fy'(x0,y0)(y-y0). Here in this problem we have x0=0 and y0=1. What is the corresponding value of z0?)(3) Find the directional derivative of f in the direction of v, when (x,y)=(0,1).(Hint: Is v a unit vector? If not yet, first convert it to a unit vector u. Then compute Duf(0,1).)