Question: Test under which conditions a derivative is negative

Hey guys,

I have the following problem:

I would like to know whether the derivative (e) is negative (given certain assumptions). 

e := diff(((d1-pfw1*Kw-pfs1*Ks-1/3*(d1-pfw1*Kw-pfs1*Ks+d2-pfw2*Kw-pfs2*Ks+d3-pfw3*Kw-pfs3*Ks))*(pf1w-1/3*(pfw1+pfw2+pfw3))+(d2-pfw2*Kw-pfs2*Ks-1/3*(d1-pfw1*Kw-pfs1*Ks+d2-pfw2*Kw-pfs2*Ks+d3-pfw3*Kw-pfs3*Ks))*(pf2w-1/3*(pfw1+pfw2+pfw3))+(d3-pfw3*Kw-pfs3*Ks-1/3*(d1-pfw1*Kw-pfs1*Ks+d2-pfw2*Kw-pfs2*Ks+d3-pfw3*Kw-pfs3*Ks))*(pf3w-1/3*(pfw1+pfw2+pfw3)))/(sqrt((d1-pfw1*Kw-pfs1*Ks-1/3*(d1-pfw1*Kw-pfs1*Ks+d2-pfw2*Kw-pfs2*Ks+d3-pfw3*Kw-pfs3*Ks))^2+(d2-pfw2*Kw-pfs2*Ks-1/3*(d1-pfw1*Kw-pfs1*Ks+d2-pfw2*Kw-pfs2*Ks+d3-pfw3*Kw-pfs3*Ks))^2+(d3-pfw3*Kw-pfs3*Ks-1/3*(d1-pfw1*Kw-pfs1*Ks+d2-pfw2*Kw-pfs2*Ks+d3-pfw3*Kw-pfs3*Ks))^2)*sqrt((pf1w-1/3*(pfw1+pfw2+pfw3))^2+(pf2w-1/3*(pfw1+pfw2+pfw3))^2+(pf3w-1/3*(pfw1+pfw2+pfw3))^2)), Kw);

Bute when I test the following...

`assuming`([type(e, negative)], [d1 > 0, d2 > 0, d3 > 0, Kw > 0, Ks > 0, 0 < pfw1 and pfw1 < 1, 0 < pfw2 and pfw2 < 1, 0 < pfw3 and pfw3 < 1, 0 < pfs1 and pfs1 < 1, 0 < pfs2 and pfs2 < 1, 0 < pfs3 and pfs3 < 1, d1-pfw1*Kw-pfs1*Ks > 1, d2-pfw2*Kw-pfs2*Ks > 1, d3-pfw3*Kw-pfs3*Ks > 1, pfw1 <> pfw2 and pfw2 <> pfw3, pfs1 <> pfs2 and pfs2 <> pfs3]);

...I get the following error message:

"Error, (in assuming) when calling '`property/ConvertProperty`'. Received: 'true is an invalid property'"

My questions are:

1.) What is the problem with the assumptions made in the type statement?

2.) Is there a way to find out under which conditions the derivative e is negative?

It would be very nice if you could help me. Thank you very much in advance!