1-If f (x,y) = x^2+2xy^2+y^2 what is the rate of change of the slope of the line tangent to f in the x direction as you move in the y direction from the point (1,-1)? 2-If f (x,y) = x^2 sin(y), x(s,t) = s^2-t^2 and y(s,t) = st, use the chain rule to find fs as a function of s, t. Let f (t) be a function such that f \'\' (5) = - 2 and let w(x,y)=f (x^2-4y). Determine ((?2w)/(?x?y)) (1,-1). Solution f (x,y) = x^2+2xy^2+y^2 df(x,y)/dx = 2x + 2y^2 = 2 + 2 = 4 slope = 4 2) f (x,y) = x^2 sin(y), x(s,t) = s^2-t^2 and y(s,t) = st f(s,t) = ( s^2-t^2)^2 sin(st).