Partial integration - correct solutions?
Let f(x; y; z) = (x^3+3xy^2-3xyz-z^4)/(x^2 + z^2)
I suppose that the solution for the partial derivative of the function to x is too simple as I get: 3(x^2+y^2-yz)/2x
Am I right when I have to use the quotient rule? as it is f´g - g´f / g^2......But what is then g only x^2 or x^2+z^2 and is f (x^3+3xy^2-3xyz-z^4) or just (x^3+3xy^2-3xyz) (as the unused variables are held constant?
so is this approach correct:
(3x^2+3y^2-3yz)*(x^2) - 2x(x^3+3xy^2-3xyz) / x^4
thank you in advance....
Re: Partial integration - correct solutions?
Re: Partial integration - correct solutions??
So am I right that u`(x) equals:
(3x^2+3y^2-3yz)*(x^2+z^2) - 2x(x^3+3xy^2-3xyz-z^4) / (x^2 + z^2)^2
so is the correct answer for u´(x):
for u´(y) I got:
for u`(z) I got:
I hope someone can confirm these solutions ;-)
Thx a lot