If $x^xy^yz^z$ = constant, then $\frac{dz}{dx}$ is equal to :

Question

( A ) $-\frac{(1+ \log_e z)}{(1 + \log_e x)}$
( B ) $x^yy^y$
( C ) $-\frac{(1+ \log_e x)}{(1 + \log_e z)}$
( D ) $x^z y^y z$