I am trying to calculate the derivative of y = e^(x*y)
Hand calculation give me the result of dy/dx = ( y*e^(x*y) ) / ( 1 - x*e^(x*y) )
But the sage is giving me the wrong output of -y/x. Here is my code:
sage:
sage: y=function('y')(x)
sage: y
y(x)
sage:
sage: expr = exp(1)**(x*y)
sage:
sage: diff(y)
diff(y(x), x)
sage:
sage: diff(expr)
(x*diff(y(x), x) + y(x))*e^(x*y(x))
sage:
sage: solve(diff(expr), diff(y))
[diff(y(x), x) == -y(x)/x]
sage:
sage:
