MathCastle
Multivariable CalculusMediumThe Chain Rule & Implicit Differentiation

The Chain Rule & Implicit Differentiation · Medium problem

Let g(u,v)=f(eu+sin⁡v, eu+cos⁡v)g(u,v) = f\big(e^u + \sin v,\ e^u + \cos v\big), where ff is differentiable with fx(1,2)=4f_x(1,2) = 4 and fy(1,2)=−3f_y(1,2) = -3. Find gv(0,0)g_v(0,0).