Question

Find the first principle f(x)=1/x
​

Answer 1

see explanation

Explanation:

Assuming you require the derivative of f(x) from first principles, then

f' (x) =
`lim_(h>0)`
`(f(x+h)-f(x))/(h)`

=
`lim_(h>0)`
`((1)/((x+h))-(1)/(x) )/(h)`

=
`lim_(h>0)`
`((x-(x+h))/(x(x+h)) )/(h)`

=
`lim_(h>0)`
`((x-x-h)/(x(x+h)) )/(h)`

=
`lim_(h>0)`
`(-h)/(hx(x+h))` ← cancel h on numerator/ denominator

= -
`(1)/(x^2)`