What is the derivative of sin 2x and cot x? - Teachoo - Examples

Example 21 - Chapter 13 Class 11 Limits and Derivatives - Part 2

 

 

  1. Chapter 13 Class 11 Limits and Derivatives (Term 1 and Term 2)
  2. Serial order wise

Transcript

Example 21 Compute derivative of (i) f(x) = sin 2x Let f (x) = sin 2x = 2 sin x cos x Let u = 2 sin x & v = cos x So, f(x) = uv ∴ f’(x) = (uv)’ = u’v + v’u Here, u = 2 sin x u’ = 2 cos x & v = cos x v’ = – sin x f’(x) = (uv)’ = u’v + v’ u = 2 cos x . cos x + 2 sin x ( – sin x) = 2 cos2 x – 2 sin2 x = 2 (cos2 x – sin2 x) ∴ f’(x) = 2 (cos2 x – sin2 x) (𝐷𝑒𝑟𝑖𝑣𝑎𝑡𝑖𝑣𝑒 𝑜𝑓 𝑠𝑖𝑛⁡〖𝑥=𝑐𝑜𝑠⁡𝑥 〗) (𝐷𝑒𝑟𝑖𝑣𝑎𝑡𝑖𝑣𝑒 𝑜𝑓 𝑐𝑜𝑠⁡〖𝑥=〖− 𝑠𝑖𝑛〗⁡𝑥 〗)

About the Author

Davneet Singh's photo - Teacher, Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.