Derivative of Natural Log Function f(x) = (x ln x)^2

[kimmy_koo51]

If f(x) = (x ln x)^2 then find all the points at which the graph of f(x) has a horizontal tangent.

I know how to do this, but I have no idea how to differentiate that.

 

[skeeter]

chain rule and product rule ...

f(x) = [x ln(x)]²

f'(x) = 2[x ln(x)]*[x * (1/x) + ln(x)]

f'(x) = 2x*ln(x)[1 + ln(x)]

set f'(x) = 0 ...

ln(x) = 0, ln(x) = -1 ...

x = 1, x = 1/e

edit: yes, you are correct tkh ... x = 0 is not in the domain of the original function ... mea culpa.

 

[tkhunny]

0?