implicit differentiation
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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