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Thanks very much for all those who replied. I really appreciate it. Unfortunately for the more complicated function that I had, the procedure did not work. It just returned the expression back to me. Perhaps, this is because the expression is not negative as I was hoping it to be, or perhaps because Mathematica could not do it. I don't know which one. Just for information I am writing down the expression I wanted to check this for. Suppose U[p,d,rl,rh] = (Log[1+p*d*rh] / Log[1+p*d*rl]) where, 0.2<p<1, 2<d<20, rl > rh > 0. I wanted to find whether the second partial derivative of this with respect to d is negative. Also, if cross partial with respect to (d,p) is negative at least for large enough 'p'. For small, p, it can be seen the ross partial can be positive or negative, which explains why Mathematica just returns the expression. Thanks once again to all who replied. These techniques will definitely be useful to me for other work. Bharat.