Finding second order derivatives - Normal form

Chapter 5 Class 12 Continuity and Differentiability
Concept wise

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### Transcript

Ex 5.7, 8 Find the second order derivatives of the function γπ‘ππγ^(β1) π₯ Let y = γπ‘ππγ^(β1) π₯ Differentiating π€.π.π‘.π₯ . ππ¦/ππ₯ = (π(γπ‘ππγ^(β1) π₯))/ππ₯ ππ¦/ππ₯ = 1/(1 + π₯^2 ) Again Differentiating π€.π.π‘.π₯ π/ππ₯ (ππ¦/ππ₯) = π/ππ₯ (1/(1 + π₯^2 )) (π^2 π¦)/(ππ₯^2 ) = π/ππ₯ (1/(1 + π₯^2 )) Using Quotient Rule As, (((π’)β²)/π£) = (π’βπ£ β π£βπ’)/π£^2 where u = 1 & v = 1 + x2 (π^2 π¦)/(ππ₯^2 ) = ((π(1))/ππ₯ (1+π₯^2 ) β (π (1 +π₯^2 ))/ππ₯ . 1 )/(1+π₯^2 )^2 (π^2 π¦)/(ππ₯^2 ) = (0 . (1+π₯^2 ) β ((π(1))/ππ₯ + (πγ(π₯γ^2))/ππ₯). 1 )/(1+π₯^2 )^2 (π^2 π¦)/(ππ₯^2 ) = (0 β ( 0 + 2π₯ ) 1)/(1+π₯^2 )^2 (π^π π)/(ππ^π ) = (βππ)/(π+π^π )^π

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#### 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.