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Misc 2 - Differentiate sin3 x + cos6 x - Chapter 5 Class 12 - 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 2 Differentiate 𝑤.𝑟.𝑡. 𝑥 the function sin﷮3﷯ 𝑥 + cos﷮6﷯ 𝑥 Let 𝑦= sin﷮3﷯ 𝑥 + cos﷮6﷯ 𝑥 Differentiating 𝑤.𝑟.𝑡.𝑥. 𝑑𝑦﷮𝑑𝑥﷯ = 𝑑 sin﷮3﷯ 𝑥 ﷯ + cos﷮6﷯ 𝑥 ﷯﷯﷮𝑑𝑥﷯ = 𝑑 sin﷮3﷯ 𝑥 ﷯﷯﷮ 𝑑𝑥﷯ + 𝑑 cos﷮6﷯ 𝑥 ﷯﷯﷮𝑑𝑥﷯ = 3 sin﷮2﷯𝑥 . 𝑑 sin﷮𝑥﷯﷯﷮𝑑𝑥﷯ + 6 cos﷮5﷯𝑥 . 𝑑 cos﷮𝑥﷯﷯﷮𝑑𝑥﷯ = 3 sin﷮2﷯𝑥 . cos﷮𝑥﷯ + 6 cos﷮5﷯𝑥. − sin﷮𝑥﷯﷯ = 3 sin﷮2﷯𝑥 . cos﷮𝑥﷯ – 6 sin﷮𝑥﷯. cos﷮5﷯𝑥 = 3 sin﷮2﷯𝑥 . cos﷮𝑥﷯ sin﷮𝑥﷯−2 cos﷮4﷯﷮𝑥﷯﷯ Hence, 𝒅𝒚﷮𝒅𝒙﷯ = 3 𝒔𝒊𝒏﷮𝒙﷯ 𝒄𝒐𝒔﷮𝒙﷯ 𝒔𝒊𝒏﷮𝒙﷯−𝟐 𝒄𝒐𝒔﷮𝟒﷯﷮𝒙﷯﷯

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