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Question
Find the derivative of the following function from first principle:
−x
Solution
Let f(x) = –x Accordingly, f(x + h) = -(x + h)
By first principle,
f'(x) = `lim_(h->0)(f(x + h) -f(x))/h`
= `lim_(h->0)(-(x + h) -(-x))/h`
= `lim_(h->0)(-x - h + x)/h`
= `lim_(h->0)(-h)/h`
= `lim_(h->0) (-1) -1`
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