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Question
Differentiate of the following from first principle:
− x
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Solution
\[\frac{d}{dx}\left( f\left( x \right) \right) = \lim_{h \to 0} \frac{f\left( x + h \right) - f\left( x \right)}{h}\]
\[\frac{d}{dx}\left( - x \right) = \lim_{h \to 0} \frac{- \left( x + h \right) - \left( - x \right)}{h}\]
\[ = \lim_{h \to 0} \frac{- x - h + x}{h}\]
\[ = \lim_{h \to 0} \frac{- h}{h}\]
\[ = \lim_{h \to 0} - 1\]
\[ = - 1\]
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