Ex 5.2, 1 - Differentiate sin (x2 + 5) - Finding derivative of a function by chain rule

  1. Chapter 5 Class 12 Continuity and Differentiability
  2. Serial order wise
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Ex 5.2, 1 Differentiate the functions with respect to 𝑥 sin⁡(𝑥2 + 5) Let 𝑓(𝑥) = sin⁡(𝑥2 + 5) y = sin (x2 + 5) We need to find derivative of 𝑦, 𝑤.𝑟.𝑡.𝑥 𝑑𝑦 ﷮𝑑𝑥﷯ = 𝑑( sin﷮ 𝑥2 + 5﷯﷯)﷮𝑑𝑥﷯ = cos 𝑥2 + 5﷯ × 𝑑 𝑥2 + 5﷯﷮𝑑𝑥﷯ = cos 𝑥2 + 5﷯ × 𝑑(𝑥2)﷮𝑑𝑥﷯+ 𝑑(5)﷮𝑑𝑥﷯﷯ = cos 𝑥2 + 5﷯ × ( 2𝑥﷮2−1﷯ + 0) = cos 𝑥2 + 5﷯ × 2𝑥 = 𝟐𝒙 𝒄𝒐𝒔﷮ (𝒙𝟐 + 𝟓)﷯

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