00:01
F of x given as x power ln of x.
00:05
So, first we have to find for part a f dash of x.
00:11
Let us take ln both sides.
00:14
So, we have ln of f of x is equals to this becomes ln of x into ln of x and this is basically ln of x whole square.
00:29
Next, now we differentiate.
00:32
So, differentiating this is 1 over f of x into f dash of x that becomes 2 times ln of x into differentiation of ln of x which is 1 by x.
00:46
So, we have simply f dash of x is equals to f x that side.
00:50
So, this is x power ln of x into ln of x by x.
00:56
So, this is the differentiation.
01:01
Next, we want to know the intervals in which it is increasing or decreasing.
01:07
So, note that f dash of x becomes equals to 0 only when ln x is 0 which means when x is equals to 1.
01:22
So, at x equals to 1 this becomes 0.
01:24
So, if we look at the number line from 0 to infinity we have 1 here and this side values are negative and this side the values are positive...