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Question: implicit differentiation

Question:implicit differentiation

longrob 1409 Maple
January 03 2010
1
Hi all Given the relation, x sin(xy)=x , and wishing to find dy/dx by implicit differentiation, the easiest and most obvious way is to cancel x and then arrive at the answer dy/dx = -y/x: > implicitdiff(sin(x*y)=1,y,x); - y/x (assuming x is not equal to 0 of course) But, what if we try this: > implicitdiff(x*sin(x*y)=x,y,x); sin(x y) + x cos(x y) y - 1 - ------------------------------- x^2 cos(x y) (with the additional assumption that cos(xy) is also not equal to zero). I can simplify this to -y/x by hand (using the 2 assumptions) but is there a way to get maple to do the same ? Thanks
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