Partial Derivative of U: sin^-1(x/y) + cos(y/x)

[ksurabhi]

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.


thank you in advance

 

[abitslow]

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]

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

... if only there was some special way you could search for a list of derivatives with your computer.

Please show your best attempt - or try to tell us about your doubt.
Otherwise we cannot know what your problem is.