Quandaries and Queries Hi please can you help? Your name. Richard Who you are, a student, a teacher, a parent, other? A teacher doing personal research The level of the question :secondary (10-12)+ Question: I need to convince myself that I understand  the process  of differentiating y=xx. The specific question is that if I have to take the logarithm of both sides of the equation how can differentiate the following? y= {(x+2)(x+2)}/{(x+1)(x+1)} - {(x+1)(x+1)}/(xx), I have an idea that the differential of this fairly complex function is itself ... am I right or wrong. Hi Richard, I would let y1 = {(x+2)(x+2)}/{(x+1)(x+1)} and y2 = {(x+1)(x+1)}/(xx) and differentiate each separately and then y' = y1' - y2' To differentiate y1 first take the natural log of both sides ln( y1) = ln( (x+2)(x+2)) - ln((x+1)(x+1)) = (x+2)ln(x+2) - (x+1)ln(x+1) Now differentiate both sides  y1'/y1 = (1 + ln(x+2)) - (1 + ln(x+1)) = ln(x+2) - ln(x+1) = ln[(x+2)/(x+1)] so y1' = y1{ln(x+2) - ln(x+1)} = {(x+2)(x+2)}/{(x+1)(x+1)}ln[(x+2)/(x+1)] Now find y2' and y' = y1' - y2'. As you will see y and y' are different. Penny Go to Math Central