Question

Multivariable Calculus,

https://www.dropbox.com/s/x0vwzhtcbj5j2fl/2014-05-03%2011.11.06.jpg


Exercise 61,

Please help me do it?

Answer 1

treat \(y\) as constant when u work \(\dfrac{\partial z}{\partial x}\)

Answer 2

thats what i see https://www.dropbox.com/s/uq2e8gjouxmygf6/Screenshot%202014-05-03%2011.53.34.jpg

Answer 3

http://prntscr.com/3fplo1

Answer 4

i think latex is not working..

Answer 5

could you please help me solve this one only just so that I get the idea please???

Answer 6

(x^2+y^2+z^2)^(3/2) = 1

simplify the equation a bit :
x^2+y^2+z^2 = 1

Answer 7

next, differentiate both sides with.respect.to "x"

Answer 8

just treat "y" as constant

Answer 9

as @ganeshie8 says, the answer would be
\[2x + 2z \frac{\partial z}{\partial x} = 0 \Rightarrow \frac{\partial z}{\partial x} = - x / z\]
if $$z \neq 0$$
undefined otherwise