# Math Help - Find deltaz/deltax and deltaz/deltay?

1. ## Find deltaz/deltax and deltaz/deltay?

here is what I am trying to do!

R=ln(u^2 + v^2 + w^2)

u= (x+2y)
v=(2x-y)
w=(2xy)

find deltaz/deltax and deltaz/deltay when x=y=1

This is a chain rule case correct? So:
Dr/dx=(1/((x+2y)^2+(2x-y)^2+(2xy)^2))(2(x+2y)(1)+2(2x-y)(2)+2(2xy)(2y))
Then placing 1 in all x and y makes:
Dr/dx=(14/9)?

And another one is:
let x^2 +y^2 +z^2=3xyz
find dz/dx and dz/dy

for this do I isolate z and then find dz/dx and dz/dy?

thanks!

2. Are you trying to find $\frac{dr}{dx}$ or $\frac{\Delta r}{\Delta x}$? You say it is the latter but calculate the former.
If you are looking for $\frac{dr}{dx}$ then, yes, the chain rule is the right way to go.

for the second, don't isolate z, use implicit differentiation: $2x+ 2z z_x= 3yz+ 3xyz_x$. Solve for $z_x$. Do the same to find $z_y$.