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LIMITS AND DERIVATIVES — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSLIMITS AND DERIVATIVES1 Mark
Question
Find the derivative of function -x from first principle.
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Answer

Here f (x) = -x
Then (f(x + h) = -(x + h)
We known that $\mathop {\lim }\limits_{h \to 0} \frac{{ - (x + h) - ( - x)}}{h} = \mathop {\lim }\limits_{h \to 0} \frac{{ - x - h + x}}{h}$
$= \mathop {\lim }\limits_{h \to 0} \frac{{ - h}}{h} = - 1$

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