# Partial derivative

if U = sin^-1 (x/y) +cos(y/x) then Ux/Uy = ?

ans is -y/x.

i have specially doubt on the partial derivative of U w.r.t y for inverse sin.

U/U=1. Ux/Uy = x/y. There is a separate homework forum. We do not do homework here.
The derivative is the sum of the partial derivatives. Any partial derivative is determined by considering all other variables as constant. dSin(x/y) would be = ∂(sin(cx))dx + ∂(sin(k/y))dy where I used c and k to emphasize that the other variable is considered constant during the differentiation of that term.

Simon Bridge