Question

Can someone show me way of solving this​

Answer 1

Explanation:

`f(x) = ln( (1)/(x) )`

To find the derivative, notice we have a function 1/x inside of another function, ln(x)

We use what we call the chain rule,

It states that

derivative of a '

`(d)/(dx) f(g(x)) = f '(g(x)) * \: g '(x)`

Here f is ln(x)

f is 1/x

So first, we know that

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

so

`f'(g(x)) = (1)/( (1)/(x) )`

We know that

`g'(x) = - \frac{1}{ {x}^(2) }`

So we have

`x * - \frac{1}{ {x}^(2) } = ( - 1)/(x)`