Why is numden not working when there is an exponential as denominator?

Hey,

I am trying to separate the nominator and denominator with the matlab function numden(). This is the code

 syms x y

 f = (x^3*y+5*x^2*y)/(exp(x^2+3*y^4));

 fx=diff(f,x);
 fx = simplify(fx)

 [fx_n,fx_d]=numden(fx)

The problem is that it gives as output

 fx_n = (x*y*(- 2*x^3 - 10*x^2 + 3*x + 10))/exp(x^2 + 3*y^4)
 fx_d = 1

While I want it to be like

 fx_n = (x*y*(- 2*x^3 - 10*x^2 + 3*x + 10))
 fx_d = exp(x^2 + 3*y^4)

If exp is changed to anything else, like cos, sin, tan or something else it is working but not for exp.

Thank you for your help.

Regards

[Wouter Donders]

Not sure what causes this behaviour other than that Matlab parses the divison by the exponent as a multiplication by its reciprocal. A workaround is by not using the exp function itself but it's definition:

   syms x y e
   f = (x^3*y+5*x^2*y)/(e^(x^2+3*y^4));
   fx=diff(f,x);
   fx = simplify(fx)
   [fx_n,fx_d]=numden(fx)

This will yield:

fx_n = x*y*(- 2*log(e)*x^3 - 10*log(e)*x^2 + 3*x + 10)
fx_d = e^(x^2)*e^(3*y^4)