Check Full Chapter Explained - Continuity and Differentiability - Application of Derivatives (AOD) Class 12



  1. Chapter 6 Class 12 Application of Derivatives
  2. Concept wise
  3. Finding rate of change


Example 1 Find the rate of change of the area of a circle per second with respect to its radius r when r = 5 cm. We have to find rate of change of area of circle with respect to radius i.e. we need to find (๐‘‘(๐ด๐‘Ÿ๐‘’๐‘Ž ๐‘œ๐‘“ ๐‘๐‘–๐‘Ÿ๐‘๐‘™๐‘’))/(๐‘‘ (๐‘Ÿ๐‘Ž๐‘‘๐‘–๐‘ข๐‘  ๐‘œ๐‘‘ ๐‘๐‘–๐‘Ÿ๐‘๐‘™๐‘’)) = ๐‘‘๐ด/๐‘‘๐‘Ÿ We know that Area of circle = ฯ€ r2 A = ฯ€r2 Finding ๐‘‘๐ด/๐‘‘๐‘Ÿ ๐‘‘๐ด/๐‘‘๐‘Ÿ = (๐‘‘(๐œ‹๐‘Ÿ2))/๐‘‘๐‘Ÿ = ฯ€ ((๐‘Ÿ2))/๐‘‘๐‘Ÿ = ฯ€ (2r) = 2ฯ€ r For r = 5 cm ๐‘‘๐ด/๐‘‘๐‘Ÿ = 2ฯ€ (5) . ๐‘๐‘š2/๐‘๐‘š = 10ฯ€ ๐’„๐’Ž๐Ÿ/๐’„๐’Ž As dimension of area is cm2 & dimension of Radius is cm

Finding rate of change

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.