Find the first order partial derivatives. z=ln(xy-sqrt(x^2-y^2)

Answer 1

so, do you mean

ln(xy-sqrt(x^2-y^2))
or
ln(xy)-sqrt(x^2-y^2)

I will assume the first, since the 2nd is much easier

∂z/∂x = 1/ln(xy-√(x^2-y^2)) * (y-x/√(x^2-y^2))

and similarly for y.