Question

Using differentiation from first principle rule prove how to find the derivative of f(x)=u(x)-v(x), when v'(x) and u'(x) are known

Answer 1

f'(x)=u'(x)-v'(x)...

Answer 2

yahh i know that.. haha but how do you prove this??

Answer 3

Alright, let y=u+v, then
y+dy=(u+du)+(v+dv) for infinitesimal distances; since dy=du+dv, as y=u+v can be taken out from the equation, dividing by dx will result in dy/dx=du/dx+dv/dx, and voila!

Answer 4

Using differentiation from first principle rule
I think they want you to use
\[\frac{df}{dx}= \lim_{\Delta x \rightarrow 0}\frac{f(x+ \Delta x)-f(x)}{\Delta x}\]