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Ex 5.6, 1 - Find dy/dx, x = 2at2, y = at4 - Class 12 - Derivatives in parametric form

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  1. Chapter 5 Class 12 Continuity and Differentiability
  2. Serial order wise
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Ex 5.6, 1 If x and y are connected parametrically by the equations without eliminating the parameter, Find ๐‘‘๐‘ฆ๏ทฎ๐‘‘๐‘ฅ๏ทฏ, x = 2 ๐‘Ž๐‘ก๏ทฎ2๏ทฏ, y = ๐‘Ž๐‘ก๏ทฎ4๏ทฏ ๐‘‘๐‘ฆ๏ทฎ๐‘‘๐‘ฅ๏ทฏ = ๐‘‘๐‘ฆ๏ทฎ๐‘‘๐‘ฅ๏ทฏ ร— ๐‘‘๐‘ก๏ทฎ๐‘‘๐‘ก๏ทฏ ๐‘‘๐‘ฆ๏ทฎ๐‘‘๐‘ฅ๏ทฏ = ๐‘‘๐‘ฆ๏ทฎ๐‘‘๐‘ก๏ทฏ ร— ๐‘‘๐‘ก๏ทฎ๐‘‘๐‘ฅ๏ทฏ ๐‘‘๐‘ฆ๏ทฎ๐‘‘๐‘ฅ๏ทฏ = ๐‘‘๐‘ฆ๏ทฎ๐‘‘๐‘ก๏ทฏ๏ทฎ ๐‘‘๐‘ฅ๏ทฎ๐‘‘๐‘ก๏ทฏ๏ทฏ Now, ๐‘‘๐‘ฆ๏ทฎ๐‘‘๐‘ฅ๏ทฏ = ๐‘‘๐‘ฆ๏ทฎ๐‘‘๐‘ก๏ทฏ๏ทฎ ๐‘‘๐‘ฅ๏ทฎ๐‘‘๐‘ก๏ทฏ๏ทฏ Putting values ๐‘‘๐‘ฆ๏ทฎ๐‘‘๐‘ฅ๏ทฏ = 4๐‘Ž ๐‘ก๏ทฎ3๏ทฏ๏ทฎ4๐‘Ž๐‘ก๏ทฏ ๐’…๐’š๏ทฎ๐’…๐’™๏ทฏ = t2

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