11 13 2235The instantaneous rate of change of f depends not onlyon the input point but also the direction in whichwe move from the input pointIffthese points all havedifferent slopesThe partial derivative of f wrt x at Xo yodenoted fx Xo yo isTx f x yo ly I Fx Xo yo Lingo tlxothiyohflxo.beThis isjust the normal derivative w rt x of f x yo towe can also apply this to yf x y x2y3 5xe3 Compute fy and fyYo Yoday f x yo y yoEx4243 5xe3y 2xy 5e3oFy f x y y y day x.ly 5xoe3y 3y xiI5x.eYfxlxy 2xy3 5e3y fy x y 3 242 15 039 35Lecture 35 Problems1 f x y x'ye C fx lil and defy lilat f x 1 the function is x'extdifferentiating wrt x day x2ext 2x ext t y extat x 1 this gives 36 II2 f x y 9114,71 what is felt 0Etake 9 0tax EMEA Incited3 f x y sin xy x3y yglx y fx x y yeas Xy Zyxh x y gy x y cos xy xysin xy 3 2