Find the derivative of the functions from first principle: –x ​​​​​​​

Let f(x) = –x. Accordingly, f(x + h) = –(x + h) By first principle,

\( f'(x)=\lim\limits_{h \to 0}\dfrac{f(x+h)-f(x)}{h}\)

\(\lim\limits_{h \to 0}\dfrac{-(x+h)-(-x)}{h}\)

\( \lim\limits_{h \to 0}\dfrac{-x-h+x}{h}\)

\( \lim\limits_{h \to 0}\dfrac{-h}{h}\)

\( \lim\limits_{h \to 0}(-1)=-1\)