Knowing that function [FONT=MathJax_Math-italic]f[FONT=MathJax_Main]([/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main],[/FONT][FONT=MathJax_Math-italic]y[/FONT][FONT=MathJax_Main])[/FONT]f(x,y)[/FONT] satisfies f_x(48,8) = -3 , f_y (48,8) = -4

And that function g(s,t) = f(3s^2*t^2, -2*s*t)

What are g_s(-2,2) and g_t(-2,2) ?

What I've done so far is conclude that g_s(s,t) = f(6*s*t^2, -2*t) and g_t(s,t) = f(6*s^2*t, -2s)

And g_s(-2,2) = f(48,4) , g_t(-2,2) = f(-48,-4)

Am I on the right path? Can tangent plane equation help ? I'm stuck, thanks.