I am stuck on explaining how to use the definition to find the derivative of lnyx in the following situation. I have to define the area under a curve

y=1/x in the terms of the natural logarithm function. wThe area under the curve f(x) is defined as the integral f(x) dx, if f(x)=1/x. Then the area under the curve is log1/x dx which equals ln lxl. So where do i go from here as far as explaining how to use the definition to find the derivative of lnyx? Any help?

On a related note, how do would you use the derivative formula from above to prove ln(a)+ln(b)= ln(ab)?

Thank you for any help in advance.