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partial diff question

f(x,y) =x[arcsin(x/y)]

find partial (df/dy) at constant x. when i differentiate x i get 0, when i differentiate arcsin(x/y) woul di be correct in saying that the partial derivitive would be

1/[(y^2 - x^2)^0.5]

cheers
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Avatar for lucaz
lucaz
OP
1
anyone
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Avatar for nota bene
nota bene
15
I get something slightly different ∂∂y(aarcsin⁡(xy))=x2yy2−x2\frac{\partial}{\partial y} (a\arcsin(\frac{x}{y}))= \frac{x^2}{y\sqrt{y^2-x^2}}. Though I may be wrong of course...

But, I think you've dropped the x^2 in your expression, because as you treat x as a constant it doesn't mean it vanishes, just that you don't need to think about it much when differentiating. So xDy(f(x,y))=Dy(x f(x,y)) where D_y represents the partial derivative.

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