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Questions  >>  CBSE XI  >>  Math  >>  Limits and Derivatives
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Find the derivative of the following function from the first principle $ -x$

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Let $f(x) = -x$. Accordingly,$f(x+h)=-(x+h)$
By first principle,
$ f'(x) = \lim\limits_{h \to 0} \large\frac{f(x+h)-f(x)}{h}$
$ = \lim\limits_{h \to 0} \large\frac{-(x+h)-(-x)}{h}$
$ = \lim\limits_{h \to 0} \large\frac{-x-h+x}{h}$
$ = \lim\limits_{h \to 0} \large\frac{-h}{h}$
$ = \lim\limits_{h \to 0} (-1) = -1$

 

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