Question

i want to integrate this x*sqrt (a^2 - x^2)
let x= a sin z ; differentiating both side with respect to x , it becomes
1= a cos z * dz/dx
or dx = a cos z dz


if i differentiate both side with respect to z , it becomes

dx/dz =acosz
or dx = ac cos z dz

my question is which one is correct? differentiating with respect of x or with respect of z and why ?