Partial Derivatives - Multivariable Calculus + Calc III
11 13 22
35
The instantaneous rate of change of f depends not only
on the input point but also the direction in which
we move from the input point
Iff
these points all have
different slopes
The partial derivative of f wrt x at Xo yo
denoted fx Xo yo is
Tx f x yo ly I Fx Xo yo Lingo tlxothiyohflxo.be
This isjust the normal derivative w rt x of f x yo to
we can also apply this to y
f x y x2y3 5xe3 Compute fy and fy
Yo Yo
day f x yo y yo
Ex4243 5xe3y 2xy 5e3o
Fy f x y y y day x.ly 5xoe3y 3y xi
I5x.eYfxlxy 2xy3 5e3y fy x y 3 242 15 039
35
Lecture 35 Problems
1 f x y x'ye C fx lil and defy lil
at f x 1 the function is x'ext
differentiating wrt x day x2ext 2x ext t y ext
at x 1 this gives 36 II
2 f x y 91
14,71 what is felt 0
E
take 9 0
tax EMEA Incited
3 f x y sin xy x3y y
glx y fx x y yeas Xy Zyx
h x y gy x y cos xy xysin xy 3 2