Question

Multi1 Partial Derivatives question
please help

Answer 1

start by taking the deriviative of "x" for the first one and treating "y" as a constant. Use product or quotient rule.

Answer 2

then plug in the given points: (4,2)

Answer 3

use quotient rule first?

Answer 4

I would use quotient rule if you don't know how to use product rule in this.

You're second partial is: \[\frac{ (x+4y)-(x-4y) }{ (x+4y)^2 }\]

Answer 5

oh sorry, thats the first one.

Answer 6

hmmm..

Answer 7

\[
f(x,y)={u\over v}\\
u=x-4y,\qquad v=x+4y\\
f_x=\frac{u_xv-uv_x}{v^2}=?\\
f_y=\frac{u_yv-uv_y}{v^2}=?
\]

Answer 8

then plug in x=4, y=2