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Misc 5 - Differentiate cos-1 x/2 / root 2x + 7 - Class 12 - Finding derivative of Inverse trigonometric functions

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  1. Chapter 5 Class 12 Continuity and Differentiability
  2. Serial order wise
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Misc 5 Differentiate 𝑤.𝑟.𝑡. 𝑥 the function, 𝑐𝑜𝑠﷮−1 ﷯ 𝑥﷮2﷯﷮ ﷮2𝑥+7 ﷯﷯ , – 2 < 𝑥 < 2 Let 𝑦= 𝑐𝑜𝑠﷮−1 ﷯ 𝑥﷮2﷯﷮ ﷮2𝑥+7 ﷯﷯ Differentiating both sides 𝑤.𝑟.𝑡.𝑥. 𝑑𝑦﷮𝑑𝑥﷯ = 𝑑﷮𝑑𝑥﷯ 𝑐𝑜𝑠﷮−1 ﷯ 𝑥﷮2﷯﷮ ﷮2𝑥+7 ﷯﷯﷯ 𝑑𝑦﷮𝑑𝑥﷯ = 𝑑 𝑐𝑜𝑠﷮−1 ﷯ 𝑥﷮2﷯﷯ . ﷮2𝑥 + 7 ﷯ − 𝑑 ﷮2𝑥 + 7 ﷯﷯﷮𝑑𝑥﷯ . 𝑐𝑜𝑠﷮−1 ﷯ 𝑥﷮2﷯ ﷮ ﷮2𝑥+7 ﷯﷯﷮2﷯﷯ 𝑑𝑦﷮𝑑𝑥﷯ = −1﷮ ﷮1 − 𝑥﷮2﷯﷯﷮2﷯﷯﷯ . 𝑑﷮𝑑𝑥﷯ 𝑥﷮2﷯﷯ ﷮2𝑥 + 7 ﷯ − 1﷮2 ﷮2𝑥 + 7﷯﷯ . 𝑑 2𝑥 + 7﷯﷮𝑑𝑥﷯ . 𝑐𝑜𝑠﷮−1 ﷯ 𝑥﷮2﷯ ﷮ ﷮2𝑥+7 ﷯﷯﷮2﷯﷯ 𝑑𝑦﷮𝑑𝑥﷯ = −1﷮ ﷮ 4 − 𝑥﷮4﷯﷮2﷯﷯﷯ . 1﷮2﷯ ﷮2𝑥 + 7 ﷯ − 1﷮2 ﷮2𝑥 + 7﷯﷯ . 2 + 0﷯ . 𝑐𝑜𝑠﷮−1 ﷯ 𝑥﷮2﷯ ﷮ 2𝑥+7﷯﷯ 𝑑𝑦﷮𝑑𝑥﷯ = −2﷮ ﷮ 4 − 𝑥﷮2﷯﷯﷯ . 1﷮2﷯ ﷮2𝑥 + 7 ﷯ − 1﷮2 ﷮2𝑥 + 7﷯﷯ . 2 . 𝑐𝑜𝑠﷮−1 ﷯ 𝑥﷮2﷯ ﷮ 2𝑥+7﷯﷯ 𝑑𝑦﷮𝑑𝑥﷯ = − ﷮2𝑥 + 7 ﷯﷮ ﷮ 4 − 𝑥﷮2﷯﷯﷯ − . 𝑐𝑜𝑠﷮−1 ﷯ 𝑥﷮2﷯﷮2 ﷮2𝑥 + 7﷯﷯ ﷮ 2𝑥+7﷯﷯ 𝑑𝑦﷮𝑑𝑥﷯ = − ﷮2𝑥 + 7 ﷯ − ﷮2𝑥 + 7 ﷯﷯ + 𝑐𝑜𝑠﷮−1 ﷯ 𝑥﷮2﷯ ﷮ 4 − 𝑥﷮2﷯﷯﷯﷮ 2𝑥 + 7﷯ − ﷮2𝑥 + 7 ﷯﷯ ﷮ 4 − 𝑥﷮2﷯﷯﷯﷯ 𝑑𝑦﷮𝑑𝑥﷯ = − ﷮2𝑥 + 7 ﷯﷯﷮2﷯﷮ 2𝑥 + 7﷯ − ﷮2𝑥 + 7 ﷯﷯ ﷮ 4 − 𝑥﷮2﷯﷯﷯﷯+ 𝑐𝑜𝑠﷮−1 ﷯ 𝑥﷮2﷯ ﷮ 4 − 𝑥﷮2﷯﷯﷮ 2𝑥+7﷯ − ﷮2𝑥 + 7 ﷯﷯ ﷮ 4 − 𝑥﷮2﷯﷯﷯﷯﷯ 𝑑𝑦﷮𝑑𝑥﷯ = − ﷮2𝑥 + 7 ﷯﷯﷮ 2𝑥 + 7﷯ ﷮2𝑥 + 7 ﷯ ﷮ 4 − 𝑥﷮2﷯﷯﷯+ 𝑐𝑜𝑠﷮−1 ﷯ 𝑥﷮2﷯ ﷮ 4 − 𝑥﷮2﷯﷯﷮ 2𝑥+7﷯ ﷮2𝑥 + 7 ﷯ ﷮ 4 − 𝑥﷮2﷯﷯﷯﷯ 𝒅𝒚﷮𝒅𝒙﷯ = −𝟏﷮ ﷮𝟐𝒙 + 𝟕﷯ ﷮ 𝟒 − 𝒙﷮𝟐﷯﷯﷯− 𝒄𝒐𝒔﷮−𝟏 ﷯ 𝒙﷮𝟐﷯ ﷮ 𝟐𝒙 + 𝟕﷯﷮ 𝟑﷮𝟐﷯﷯ ﷯

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Davneet Singh
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.
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