dse 2008 doubts

[Sris]

consider the eq. x^y+y^z+z^x =k defined for all +ve values of x and y and k= given +ve constant . the partial derivative dz/dx equals...

a) -(xz^x-1 +y^z lny)/yx^y-1 +z^x ln z)
b) -(yx^y-1 +z^x ln z)/xz^x-1 +y^z lny
c) -(zy^z-1 +x^y ln x)/xz^x-1 +y^z lny
d) -(zy^z-1+z^x ln z)/xz^x-1+z^x ln z)

plz help

[RS]

B.
dz/dx = -(f'x/f'z)