Misc 8 - Differentiate cos (a cos x + b sin x) - 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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Misc 8 (Method 1) Differentiate 𝑤.𝑟.𝑡. 𝑥 the function, cos ⁡(𝑎 cos⁡𝑥+𝑏 sin⁡𝑥), for some constant 𝑎 and 𝑏. Let 𝑦 = cos ⁡(𝑎 cos⁡𝑥+𝑏 sin⁡𝑥) Differentiating 𝑤.𝑟.𝑡.𝑥. 𝑑𝑦﷮𝑑𝑥﷯ = 𝑑(cos a cos﷮x﷯+b sin﷮x﷯﷯﷯﷮𝑑𝑥﷯ 𝑑𝑦﷮𝑑𝑥﷯ = − sin﷮𝑥﷯ 𝑎 cos⁡𝑥+𝑏 sin⁡𝑥﷯ . 𝑑⁡(𝑎 cos⁡𝑥+𝑏 sin⁡𝑥)﷮𝑑𝑥﷯ = − sin﷮𝑥﷯ 𝑎 cos⁡𝑥+𝑏 sin⁡𝑥﷯ . 𝑎 . 𝑑﷮ cos﷮𝑥﷯﷯﷯﷮𝑑𝑥﷯+𝑏 . 𝑑﷮ sin﷮𝑥﷯﷯﷯﷮𝑑𝑥﷯﷯ = − sin﷮𝑥﷯ 𝑎 cos⁡𝑥+𝑏 sin⁡𝑥﷯ . 𝑎 − sin﷮𝑥﷯﷯+𝑏 cos﷮𝑥﷯﷯﷯ = − sin﷮𝑥﷯ 𝑎 cos⁡𝑥+𝑏 sin⁡𝑥﷯ . − 𝑎 sin﷮𝑥﷯+𝑏 cos﷮𝑥﷯﷯ = − 𝐬𝐢𝐧﷮ 𝒂 𝒄𝒐𝒔⁡𝒙+𝒃 𝒔𝒊𝒏⁡𝒙﷯ 𝒂 𝒔𝒊𝒏﷮𝒙﷯−𝒃 𝒄𝒐𝒔﷮𝒙﷯﷯﷯

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