Question

find the derivative
y=1-ln(1/x)

Answer 1

use the chain rule
f(x)=-ln(x)
g(x)=1/x
d/dx f(g(x)) = f'(g)*g'(x)

Answer 2

$$
\cfrac{d}{dx}(1)=?
$$
That should be easy
$$
\ln x=\int_1^x\cfrac{1}{x}dx
$$
So the derivative of the integral is what?
Put these together. Problem solved.