Example 48 - Differentiate sin2 x w.r.t. ecosx - Chapter 5 - Examples

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  1. Chapter 5 Class 12 Continuity and Differentiability
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Example 48 Differentiate ๐‘ ๐‘–๐‘›๏ทฎ2๏ทฏ๐‘ฅ ๐‘ค.๐‘Ÿ.๐‘ก. ๐‘’๏ทฎcosโก๐‘ฅ . ๏ทฏ Let ๐‘ข = ๐‘ ๐‘–๐‘›๏ทฎ2๏ทฏ๐‘ฅ & ๐‘ฃ = ๐‘’๏ทฎcosโก๐‘ฅ ๏ทฏ We need to differentiate ๐‘ข ๐‘ค.๐‘Ÿ.๐‘ก. ๐‘ฃ . i.e., ๐‘‘๐‘ข๏ทฎ๐‘‘๐‘ฃ๏ทฏ ๐‘‘๐‘ข๏ทฎ๐‘‘๐‘ฃ๏ทฏ = ๐‘‘๐‘ข๏ทฎ๐‘‘๐‘ฃ๏ทฏ . ๐‘‘๐‘ฅ๏ทฎ๐‘‘๐‘ฅ๏ทฏ ๐‘‘๐‘ข๏ทฎ๐‘‘๐‘ฃ๏ทฏ = ๐‘‘๐‘ข๏ทฎ๐‘‘๐‘ฅ๏ทฏ . ๐‘‘๐‘ฅ๏ทฎ๐‘‘๐‘ฃ๏ทฏ ๐’…๐’–๏ทฎ๐’…๐’—๏ทฏ = ๐’…๐’–๏ทฎ๐’…๐’™๏ทฏ๏ทฎ ๐’…๐’—๏ทฎ๐’…๐’™๏ทฏ๏ทฏ Calculating ๐’…๐’–๏ทฎ๐’…๐’™๏ทฏ ๐‘ข = ๐‘ ๐‘–๐‘›๏ทฎ2๏ทฏ๐‘ฅ Differentiating ๐‘ค.๐‘Ÿ.๐‘ก.๐‘ฅ. ๐‘‘๐‘ข๏ทฎ๐‘‘๐‘ฅ๏ทฏ = ๐‘‘ ๐‘ ๐‘–๐‘›๏ทฎ2๏ทฏ๐‘ฅ๏ทฏ๏ทฎ๐‘‘๐‘ฅ๏ทฏ ๐‘‘๐‘ข๏ทฎ๐‘‘๐‘ฅ๏ทฏ = 2 sinโก๐‘ฅ . ๐‘‘ sin๏ทฎ๐‘ฅ๏ทฏ๏ทฏ๏ทฎ๐‘‘๐‘ฅ๏ทฏ ๐‘‘๐‘ข๏ทฎ๐‘‘๐‘ฅ๏ทฏ = 2 sinโก๐‘ฅ . cos๏ทฎ๐‘ฅ๏ทฏ

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