Last updated at Dec. 8, 2016 by Teachoo

Transcript

Ex 13.2, 10 Find the derivative of cos x from first principle. Let f (x) = cos x We need to find f’(x) We know that f’(x) = limh→0 f x + h − f(x)h Here, f (x) = cos x So, f (x + h) = cos (x + h) Putting values, f’ (x) = limh→0 𝒄𝒐𝒔 𝒙 + 𝒉 − 𝒄𝒐𝒔𝒙h Using cos A – cos B = – 2 sin 𝐴 + 𝐵2 sin 𝐴 − 𝐵2 = limh→0 −𝟐 𝒔𝒊𝒏 𝒙 + 𝒙 + 𝒉𝟐 . 𝒔𝒊𝒏 𝒙 + 𝒉 − 𝒙𝟐h = limh→0 −2 𝑠𝑖𝑛 2𝑥 + ℎ2 . 𝑠𝑖𝑛 ℎ2h = limh→0−2 sin 2𝑥 + ℎ2. sin ℎ2ℎ = limh→0− sin 2𝑥 + ℎ2. sin ℎ2 ℎ2 = limh→0− sin 2𝑥 + ℎ2. 𝐥𝐢𝐦𝐡→𝟎 𝐬𝐢𝐧 𝒉𝟐 𝒉𝟐 = limh→0− sin 2𝑥 + ℎ2.𝟏 = limh→0− sin 2𝑥 + ℎ2 Putting h = 0 = − sin 2𝑥 +02 = − sin 2𝑥2 = – sin x ∴ f’ (x) = – sin x

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.