partial differentiation

[rcd111]

hi guys wondering if u could help.

iv got a question that involves partial differentiation but it involves doing it from first prinicples

i kno the way to do normal differentiation from first principles....

dy/dx = limit as h tends to zero [f(x+h) - f(x)]/h etc etc

however i dont know what to do when its partial differentiation

the function is f(x,y,z) = 2(x^2 +z)y + x/(z^2)

hope u can help me!

rcd

[Modderman]

do you understand how you differentiate like x^2 without the limit formula?( x^2 becomes 2x.)
you need to know that before you can do partial differentiation.

When it is partial differentiation you differently 3 different times for you equation.
one for x, one for y and one for z.
for the x equation you differentiate 2(x^2 +z)y + x/(z^2) treat X as the variable and treat y&z as constants.

[Modderman]

Fx=(4·x·y·z^2 + 1)/z^2
Fy=2·(x^2 + z)
Fz=2·(y·z^3 - x)/z^3

[rcd111]

i am fully aware how to partially differentiate functions however i am being asked to do it from 1st principles and this is what is causing me problems.

[Glaysher]

It works the same way as normal differentiation from first principles as the other variables are treated as constants.