Misc 1 (i) - Chapter 12 Class 11 Limits and Derivatives

Last updated at July 31, 2026 by

Misc 1 - Find derivative by first principle: -x, sin (x+1)

Misc 1 - Chapter 13 Class 11 Limits and Derivatives - Part 2

 

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Misc 1 Find the derivative of the following functions from first principle: –x Let f (x) = – x We need to find derivative of f(x) i.e. f’ (x) We know that f’(x) = lim┬(h→0) 𝑓⁡〖(𝑥 + ℎ) − 𝑓(𝑥)〗/ℎ Here, f (x) = – x So, f (x + h) = – (x + h) Putting values f’ (x) = lim┬(h→0)⁡〖((−(x + h)) − (−x))/h〗 = lim┬(h→0)⁡〖(−𝑥 − ℎ + 𝑥)/h〗 = lim┬(h→0)⁡〖(−ℎ)/h〗 = lim┬(h→0)⁡〖(−1)〗 = –1 Hence, f’(x) = – 1

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