Question

Question #e2a9c

Answer 1

`"See explanation"`

Explanation:

`f'(x) = lim_{h->0} (f(x+h) - f(x))/h`
`"Here we have"`
`f(x) = ln(x)`
`=> f'(x) = lim_{h->0} (ln(x+h) - ln(x))/h`
`= lim_{h->0} ln((x+h)/x)/h`
`= lim_{h->0} ln(1+h/x)/h`
`= y`
`=> e^y = lim_{h->0} (1+h/x)^(1/h)`
`= e^(1/x)" (Euler's limit)"`
`=> y = 1/x`
`=> f'(x) = 1/x`