Ex 5.2, 6 - Differentiate cos x3 sin2 (x5) - Chapter 5 CBSE - Finding derivative of a function by chain rule

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  1. Chapter 5 Class 12 Continuity and Differentiability
  2. Serial order wise
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Ex 5.2, 6 Differentiate the functions with respect to 𝑥 cos⁡𝑥3 . sin2 (𝑥5) Let 𝑦 =cos⁡𝑥3 . sin2 (𝑥5) Let 𝑢 = cos⁡𝑥3 & 𝑣=sin2 (𝑥5) 𝑦 = 𝑢𝑣 We need to find derivative of 𝑦 𝑤.𝑟.𝑡.𝑥 i.e. 𝑦﷮′﷯ = 𝑢𝑣﷯﷮′﷯ 𝑑𝑦﷮𝑑𝑥﷯ = 𝑑 𝑢𝑣﷯﷮𝑑𝑥﷯ 𝑑﷮𝑑𝑥﷯ 𝑢𝑣﷯= 𝑑 𝑢﷯﷮𝑑𝑥﷯ . 𝑣+ 𝑑 𝑣﷯﷮𝑑𝑥﷯ . 𝑢 Finding 𝒖’ 𝑢=cos⁡𝑥3 Differentiating 𝑑𝑢﷮𝑑𝑥﷯ = 𝑑 cos⁡𝑥3﷯﷮𝑑𝑥﷯ = − sin﷮𝑥3﷯ . 𝑑 𝑥3﷯﷮𝑑𝑥﷯ = − sin﷮ 𝑥﷮3﷯﷯. 3 𝑥﷮3 −1﷯ = − sin﷮ 𝑥﷮3﷯﷯. 3 𝑥﷮2﷯ = − 3 𝑥﷮2﷯ . sin﷮ 𝑥﷮3﷯﷯ Now 𝑑𝑦﷮𝑑𝑥﷯ = 𝑑 𝑢﷯﷮𝑑𝑥﷯ . 𝑣+ 𝑑 𝑣﷯﷮𝑑𝑥﷯ . 𝑢 = − 3 𝑥﷮2﷯ . sin﷮ 𝑥﷮3﷯﷯﷯ . sin2 𝑥5﷯+10 𝑥﷮4﷯ . sin 𝑥﷮5﷯ . cos﷮ 𝑥﷮5﷯﷯ cos⁡𝑥3﷯ =𝟏𝟎 𝒙﷮𝟒﷯ . 𝒔𝒊𝒏 𝒙﷮𝟓﷯ . 𝒄𝒐𝒔﷮ 𝒙﷮𝟓﷯﷯. 𝒄𝒐𝒔﷮ 𝒙﷮𝟑﷯﷯− 𝟑 𝒙﷮𝟐﷯. 𝒔𝒊𝒏﷮ 𝒙﷮𝟑﷯﷯.𝒔𝒊𝒏𝟐 𝒙𝟓

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