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what is the differentiation of 1/x pls explain

what is the differentiation of 1/x pls explain

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
8 years ago
Ans: -1/x^2
Sol: Let f(x) = 1/x
Then by definition of differentiation, we have
df(x)/dx = lim(h –> 0)(([f(x+h)] – [f(x)])/ h))
df(x)/dx = lim(h → 0)(([1/(x + h)] – [1/x]/h))
df(x)/dx = lim(h → 0)(-h/h.x.(x +h))
df(x)/dx = lim(h → 0)(-1/x.(x + h))
df(x)/dx = -1/x^2
Thanks & Regards
Jitender Singh
IIT Delhi
askIITians Faculty

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