Question

How do you differentiate `f(x)=xln(1/x)-lnx/x`?

Answer 1

It is `f'(x)=ln(1/x)-1-(1-lnx)/x^2`

Explanation:

The derivative is

#d(f(x))/dx=x'*ln(1/x)+x*ln(1/x)'-((lnx)'x-x'*lnx)/(x^2)=> d(f(x))/dx=ln(1/x)+x*((1/x)'/(1/x))-(1-lnx)/x^2=> d(f(x))/dx=ln(1/x)-1-(1-lnx)/x^2#

Remember that

`d(lnx)/dx=1/x`