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Example 23 - Differentiate sin ⁡(cos ⁡(x2)) - Chapter 5 CBSE - Finding derivative of a function by chain rule

  1. Chapter 5 Class 12 Continuity and Differentiability
  2. Serial order wise
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Example 23 Differentiate sin ⁡(cos ⁡(𝑥2)) with respect to 𝑥 . Let 𝑦 = sin ⁡(cos ⁡𝑥2) We need to find derivative of 𝑦 𝑤.𝑟.𝑡.𝑥 i.e. ﷐𝑦﷮′﷯ = ﷐﷐𝑠𝑖𝑛﷮ ﷐﷐cos﷮﷐𝑥﷮2﷯﷯﷯﷯﷯ ﷐𝑑𝑦﷮𝑑𝑥﷯ = ﷐𝑑﷐﷐𝑠𝑖𝑛﷮ ﷐﷐cos﷮﷐𝑥﷮2﷯﷯﷯﷯﷯﷮𝑑𝑥﷯ = cos ﷐﷐cos﷮﷐𝑥﷮2﷯﷯﷯ . ﷐𝑑﷐﷐cos﷮﷐𝑥﷮2﷯﷯﷯﷮𝑑𝑥﷯ = cos ﷐﷐cos﷮﷐𝑥﷮2﷯﷯﷯. ﷐−﷐sin﷮﷐𝑥﷮2﷯﷯﷯ . ﷐𝑑﷐﷐𝑥﷮2﷯﷯﷮𝑑𝑥﷯ = cos ﷐﷐cos﷮﷐𝑥﷮2﷯﷯﷯. ﷐−﷐sin﷮﷐𝑥﷮2﷯﷯﷯ . 2﷐𝑥﷮2 −1﷯ = cos ﷐﷐cos﷮﷐𝑥﷮2﷯﷯﷯. ﷐−﷐sin﷮﷐𝑥﷮2﷯﷯﷯ . 2𝑥 = − 2x sin ﷐𝒙﷮𝟐﷯. cos (cos ﷐𝒙﷮𝟐﷯)

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.