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Misc 13 - Find dy/dx, if y = sin-1 x + sin-1 root 1-x2 - 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 13 Find ๐‘‘๐‘ฆ๏ทฎ๐‘‘๐‘ฅ๏ทฏ , if ๐‘ฆ= ๐‘ ๐‘–๐‘›๏ทฎโˆ’๐Ÿ๏ทฏ ๐‘ฅ+ ๐‘ ๐‘–๐‘›๏ทฎโˆ’1๏ทฏ ๏ทฎ1โˆ’๐‘ฅ2๏ทฏ, โ€“ 1 โ‰ค ๐‘ฅ โ‰ค 1 ๐‘ฆ= ๐‘ ๐‘–๐‘›๏ทฎโˆ’๐Ÿ๏ทฏ ๐‘ฅ+ ๐‘ ๐‘–๐‘›๏ทฎโˆ’1๏ทฏ ๏ทฎ1โˆ’ ๐‘ฅ๏ทฎ2๏ทฏ๏ทฏ , โ€“ 1 โ‰ค ๐‘ฅ โ‰ค 1 Put ๐‘ฅ = ๐‘ ๐‘–๐‘›โก๐œƒ ๐‘ฆ= ๐‘ ๐‘–๐‘›๏ทฎโˆ’๐Ÿ๏ทฏ sinโก๐œƒ๏ทฏ+ ๐‘ ๐‘–๐‘›๏ทฎโˆ’1๏ทฏ ๏ทฎ1โˆ’ sin๏ทฎ2๏ทฏ๐œƒ ๏ทฏ ๐‘ฆ=๐œƒ+ ๐‘ ๐‘–๐‘›๏ทฎโˆ’1๏ทฏ ๏ทฎ cos๏ทฎ2๏ทฏ๐œƒ ๏ทฏ ๐‘ฆ=๐œƒ+ ๐‘ ๐‘–๐‘›๏ทฎโˆ’1๏ทฏ cos ๐œƒ๏ทฏ ๐‘ฆ=๐œƒ+ ๐‘ ๐‘–๐‘›๏ทฎโˆ’1๏ทฏ sin๏ทฎ ๐œ‹๏ทฎ2๏ทฏ โˆ’๐œƒ๏ทฏ๏ทฏ๏ทฏ ๐‘ฆ=๐œƒ+ ๐œ‹๏ทฎ2๏ทฏ โˆ’๐œƒ๏ทฏ ๐‘ฆ=๐œƒโˆ’๐œƒ + ๐œ‹๏ทฎ2๏ทฏ ๐‘ฆ= ๐œ‹๏ทฎ2๏ทฏ Differentiating ๐‘ค.๐‘Ÿ.๐‘ก.๐‘ฅ. ๐‘‘๐‘ฆ๏ทฎ๐‘‘๐‘ฅ๏ทฏ = ๐‘‘ ๐œ‹๏ทฎ2๏ทฏ๏ทฏ๏ทฎ๐‘‘๐‘ฅ๏ทฏ ๐’…๐’š๏ทฎ๐’…๐’™๏ทฏ = 0

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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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