Check sibling questions

Example 44 - Differentiate the function (i) root (3x+2) + 1/root(2x^2

Example 44 - Chapter 5 Class 12 Continuity and Differentiability - Part 2
Example 44 - Chapter 5 Class 12 Continuity and Differentiability - Part 3
Example 44 - Chapter 5 Class 12 Continuity and Differentiability - Part 4

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Example 44 Differentiate w.r.t. x, the following function: (i) √(3𝑥+2) + 1/√(2𝑥^2+ 4) Let y = √(3𝑥+2) + 1/√(2𝑥^2+ 4 ) Differentiating 𝑤.𝑟.𝑡.𝑥 𝑑𝑦/𝑑𝑥 = 𝑑(√(3𝑥 + 2) " + " 1/√(2𝑥^2 + 4 ))/𝑑𝑥 𝑑𝑦/𝑑𝑥 = 𝑑(√(3𝑥 + 2))/𝑑𝑥 + 𝑑(1/√(2𝑥^2 + 4 ))/𝑑𝑥 𝑑𝑦/𝑑𝑥 = 𝑑(√(3𝑥 + 2))/𝑑𝑥 + (𝑑(2𝑥^2 + 4)^((−1)/2))/𝑑𝑥 Calculating 𝑑(√(3𝑥 + 2))/𝑑𝑥 & (𝑑(2𝑥^2 + 4)^((−1)/2))/𝑑𝑥 separately Calculating 𝐝(√(𝟑𝐱 + 𝟐))/𝒅𝒙 𝑑(√(3𝑥 + 2))/𝑑𝑥 = 1/(2√(3𝑥 + 2 )) × 𝑑(3𝑥 + 2)/𝑑𝑥 = 1/(2√(3𝑥 + 2 )) × (3+0) = 𝟑/(𝟐√(𝟑𝒙 + 𝟐 )) Calculating (𝒅(𝟐𝒙^𝟐 + 𝟒)^((−𝟏)/𝟐))/𝒅𝒙 (𝑑(2𝑥^2 + 4)^((−1)/2))/𝑑𝑥 = (−1)/2 〖(2𝑥^2+4)〗^((−1)/( 2) −1) . 𝑑(2𝑥^2+ 4)/𝑑𝑥 = (−1)/2 (2𝑥^2+ 4)^((−3)/( 2)) . (𝑑(2𝑥^2 )/𝑑𝑥 + 𝑑(4)/𝑑𝑥) = (−1)/2 (2𝑥^2+ 4)^((−3)/( 2)) . (4𝑥+0) = (−4𝑥)/2 (2𝑥^2+ 4)^((−3)/( 2)) = (−𝟐𝒙)/(𝟐𝒙^𝟐+ 𝟒)^(𝟑/𝟐) Hence, 𝑑𝑦/𝑑𝑥 = 𝑑(√(3𝑥+2))/𝑑𝑥 + 𝑑(1/√(2𝑥^2+ 4 ))/𝑑𝑥 𝒅𝒚/𝒅𝒙 = 𝟑/(𝟐√(𝟑𝒙 + 𝟐 )) − 𝟐𝒙/(𝟐𝒙^𝟐+ 𝟒)^(𝟑/( 𝟐))

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.