Question

Find the first principle f(x)=1/x​

Answer 1

Answer:

see explanation

Step-by-step explanation:

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

f' (x) = $lim_{h>0}$ $\frac{f(x+h)-f(x)}{h}$

       = $lim_{h>0}$ $\frac{\frac{1}{(x+h)}-\frac{1}{x} }{h}$

       = $lim_{h>0}$ $\frac{\frac{x-(x+h)}{x(x+h)} }{h}$

       = $lim_{h>0}$ $\frac{\frac{x-x-h}{x(x+h)} }{h}$

        = $lim_{h>0}$ $\frac{-h}{hx(x+h)}$ ← cancel h on numerator/ denominator

        =  - $\frac{1}{x^2}$