Quandaries and Queries


hello my name is Calebius
I am a year 12 Student
How do you differentiate y=(x)(xx)?


Hi Calebius,

Suppose that y = xg(x) and you want to differentiate y with respect to x. First take the natural log of both sides and use the properties of the log fuctions to get

ln(y) = ln( xg(x)) = g(x) ln(x)

Now differentiate both sides

 y'/y = g'(x) ln(x) + g(x)/x

and hence

y' = y [ g'(x) ln(x) + g(x)/x ] that is
y' = xg(x) [ g'(x) ln(x) + g(x)/x ]

In your problem g(x) = xx so you are going to have to use this method again to find g'(x).