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)+


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)}


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)]


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.



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