Check sibling questions

Ex 5.7, 8 - Find second order derivatives of tan-1 x - Ex 5.7

Ex 5.7, 8 - Chapter 5 Class 12 Continuity and Differentiability - Part 2

Introducing your new favourite teacher - Teachoo Black, at only β‚Ή83 per month


Transcript

Ex 5.7, 8 Find the second order derivatives of the function γ€–π‘‘π‘Žπ‘›γ€—^(βˆ’1) π‘₯ Let y = γ€–π‘‘π‘Žπ‘›γ€—^(βˆ’1) π‘₯ Differentiating 𝑀.π‘Ÿ.𝑑.π‘₯ . 𝑑𝑦/𝑑π‘₯ = (𝑑(γ€–π‘‘π‘Žπ‘›γ€—^(βˆ’1) π‘₯))/𝑑π‘₯ 𝑑𝑦/𝑑π‘₯ = 1/(1 + π‘₯^2 ) Again Differentiating 𝑀.π‘Ÿ.𝑑.π‘₯ 𝑑/𝑑π‘₯ (𝑑𝑦/𝑑π‘₯) = 𝑑/𝑑π‘₯ (1/(1 + π‘₯^2 )) (𝑑^2 𝑦)/(𝑑π‘₯^2 ) = 𝑑/𝑑π‘₯ (1/(1 + π‘₯^2 )) Using Quotient Rule As, (((𝑒)β€²)/𝑣) = (𝑒’𝑣 βˆ’ 𝑣’𝑒)/𝑣^2 where u = 1 & v = 1 + x2 (𝑑^2 𝑦)/(𝑑π‘₯^2 ) = ((𝑑(1))/𝑑π‘₯ (1+π‘₯^2 ) βˆ’ (𝑑 (1 +π‘₯^2 ))/𝑑π‘₯ . 1 )/(1+π‘₯^2 )^2 (𝑑^2 𝑦)/(𝑑π‘₯^2 ) = (0 . (1+π‘₯^2 ) βˆ’ ((𝑑(1))/𝑑π‘₯ + (𝑑〖(π‘₯γ€—^2))/𝑑π‘₯). 1 )/(1+π‘₯^2 )^2 (𝑑^2 𝑦)/(𝑑π‘₯^2 ) = (0 βˆ’ ( 0 + 2π‘₯ ) 1)/(1+π‘₯^2 )^2 (𝒅^𝟐 π’š)/(𝒅𝒙^𝟐 ) = (βˆ’πŸπ’™)/(𝟏+𝒙^𝟐 )^𝟐

Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

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.