Answer:
see explanation
Step-by-step explanation:
Assuming you require the derivative of f(x) from first principles, then
f' (x) = [tex]lim_{h>0}[/tex] [tex]\frac{f(x+h)-f(x)}{h}[/tex]
= [tex]lim_{h>0}[/tex] [tex]\frac{\frac{1}{(x+h)}-\frac{1}{x} }{h}[/tex]
= [tex]lim_{h>0}[/tex] [tex]\frac{\frac{x-(x+h)}{x(x+h)} }{h}[/tex]
= [tex]lim_{h>0}[/tex] [tex]\frac{\frac{x-x-h}{x(x+h)} }{h}[/tex]
= [tex]lim_{h>0}[/tex] [tex]\frac{-h}{hx(x+h)}[/tex] ← cancel h on numerator/ denominator
= - [tex]\frac{1}{x^2}[/tex]
