Question

Find fx(x,y), fy(x,y), fx(1,3), and fy(-2,4) for the given function. If 

𝑧 = 𝑓(𝑥, 𝑦) = 3𝑥ଷ𝑦ଶ − 𝑥ଶ𝑦ଷ + 4𝑥 + 9

Answer 1

$z=f(x,y)=3xy-xy+4x+9$

$fx(x,y)=3y-y+4$

$fy(x,y)=3x-x$

$fx(1,3)=3(3)-3+4$

$\\=6+4\\=10$

$fy(-2,4)=3(-2)-(-2)\\=-6+2\\-4$