Chapter 5 Class 12 Continuity and Differentiability
Ex 5.1, 13
Ex 5.1, 16
Ex 5.1, 18 Important
Ex 5.1, 28 Important
Ex 5.1, 30 Important
Ex 5.1, 34 Important
Ex 5.2, 5
Ex 5.2, 9 Important
Ex 5.2, 10 Important
Ex 5.3, 10 Important
Ex 5.3, 14
Example 29 Important
Example 30 Important
Ex 5.5,6 Important
Ex 5.5, 7 Important
Ex 5.5, 11 Important
Ex 5.5, 16 Important
Ex 5.6, 7 Important
Ex 5.6, 11 Important
Example 38 Important
Ex 5.7, 14 Important
Question 4 Important Deleted for CBSE Board 2025 Exams
Question 5 Important Deleted for CBSE Board 2025 Exams
Example 39 (i) You are here
Example 40 (i)
Example 42 Important
Misc 6 Important
Misc 15 Important
Misc 16 Important
Misc 22 Important
Chapter 5 Class 12 Continuity and Differentiability
Last updated at April 16, 2024 by Teachoo
Example 39 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))