# Example 17 - Chapter 13 Class 11 Limits and Derivatives

Last updated at Dec. 8, 2016 by Teachoo

Last updated at Dec. 8, 2016 by Teachoo

Transcript

Example 17 Compute the derivative tan x. Let f(x) = tan x We need to find f’ (x) We know that f’(x) = limℎ→0 f 𝑥 + ℎ − f (x)ℎ Here, f(x) = tan x So, f(x + ℎ) = tan (x + ℎ) Putting values f’ (x) = limℎ→0 tan 𝑥 + ℎ − tan𝑥ℎ f’ (x) = limℎ→0 1ℎ ( tan (x + h) – tan x) = limℎ→0 1ℎ sin 𝑥 + ℎ cos 𝑥 + ℎ − sin𝑥 cos𝑥 = limℎ→0 1ℎ cos x sin 𝑥 + ℎ − cos 𝑥 + ℎ sin𝑥 cos 𝑥 + ℎ cos𝑥 = limℎ→0 1ℎ 𝒔𝒊𝒏 𝒙 + 𝒉 𝒄𝒐𝒔𝒙 − 𝒄𝒐𝒔 𝒙 + 𝒉. 𝒔𝒊𝒏𝒙 cos 𝑥 + ℎ cos𝑥 = limℎ→0 1ℎ 𝐬𝐢𝐧 𝒙 + 𝒉 − 𝒙 cos 𝑥 + ℎ cos𝑥 = limℎ→0 1ℎ ( sin 𝑥 + ℎ − 𝑥 ) cos 𝑥 + ℎ cos𝑥 = limℎ→0 1ℎ ( sin ℎ) cos 𝑥 + ℎ cos𝑥 = limℎ→0 sinℎℎ 1 cos 𝑥 + ℎ cos𝑥 = 𝐥𝐢𝐦𝒉→𝟎 𝒔𝒊𝒏𝒉𝒉 × limℎ→0 1 cos 𝑥 + ℎ cos𝑥 = 1 × limℎ→0 1 cos 𝑥 + ℎ cos𝑥 = limℎ→0 1 cos 𝑥 + ℎ cos𝑥 Putting ℎ = 0 = 1 cos 𝑥 + 0 cos𝑥 = 1 cos x . cos𝑥 = 1 𝑐𝑜𝑠2𝑥 = sec2x Hence , f’(x) = sec2x

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.