Check Full Chapter Explained - Continuity and Differentiability - Continuity and Differentiability Class 12



Last updated at Sept. 21, 2018 by Teachoo
Check Full Chapter Explained - Continuity and Differentiability - Continuity and Differentiability Class 12
Transcript
Ex 5.5, 5 Differentiate the functions in, 𝑥 + 32 . 𝑥 + 43 . 𝑥 + 54 Let 𝑦= 𝑥 + 32 . 𝑥 + 43 . 𝑥 + 54 Taking log both sides log𝑦 = log 𝑥 + 32 . 𝑥 + 43 . 𝑥 + 54 log𝑦 = log 𝑥 + 32 + log 𝑥 + 43 + log 𝑥 + 54 log𝑦 = 2 log 𝑥 + 3 + 3 log 𝑥 + 4 + 4 log 𝑥 + 5 Differentiating both sides 𝑤.𝑟.𝑡.𝑥. 𝑑 log𝑦𝑑𝑥 = 𝑑 2 log 𝑥 + 3 + 3 log 𝑥 + 4 + 4 log 𝑥 + 5𝑑𝑥 𝑑 log𝑦𝑑𝑥 𝑑𝑦𝑑𝑦 = 𝑑 2 log 𝑥 + 3𝑑𝑥 + 𝑑 3 log 𝑥 + 4𝑑𝑥 + 𝑑 4 log 𝑥 + 5𝑑𝑥 𝑑 log𝑦𝑑𝑦 𝑑𝑦𝑑𝑥 = 2 𝑑 log 𝑥 + 3𝑑𝑥 + 3 𝑑 log 𝑥 + 4𝑑𝑥 + 4 𝑑 log 𝑥 + 5𝑑𝑥 1𝑦 × 𝑑𝑦𝑑𝑥 = 2. 1 𝑥 + 3 . 𝑑 𝑥 + 3𝑑𝑥 + 3. 1 𝑥 + 4 . 𝑑 𝑥 + 4𝑑𝑥 + 4. 1 𝑥 + 5 . 𝑑 𝑥 + 5𝑑𝑥 1𝑦 × 𝑑𝑦𝑑𝑥 = 2𝑥 + 3 𝑑𝑥𝑑𝑥+ 𝑑 3𝑑𝑥 + 3𝑥 + 4 𝑑𝑥𝑑𝑥+ 𝑑 4𝑑𝑥 + 4𝑥 +5 𝑑𝑥𝑑𝑥+ 𝑑 5𝑑𝑥 1𝑦 × 𝑑𝑦𝑑𝑥 = 2𝑥 + 3 1+0 + 3𝑥 + 4 1+0 + 4𝑥 + 5 1+0 1𝑦 × 𝑑𝑦𝑑𝑥 = 2𝑥 + 3 + 3𝑥 + 4 + 4𝑥 + 5 𝑑𝑦𝑑𝑥 = 𝑦 2𝑥 + 3 + 3𝑥 + 4 + 4𝑥 + 5 Putting value of 𝑦 𝑑𝑦𝑑𝑥 = 𝑥 + 32 . 𝑥 + 43 . 𝑥 + 54 2 𝑥 + 3+ 3 𝑥 + 4 + 4 𝑥 + 5 𝑑𝑦𝑑𝑥 = 𝑥 + 32 𝑥 + 43 𝑥 + 54 2 𝑥 + 4 𝑥 + 5 + 3 𝑥 + 3 𝑥 + 5 + 4 𝑥 + 3 𝑥 + 4 𝑥 + 3 𝑥 + 4 𝑥 + 5 𝑑𝑦𝑑𝑥 = 𝑥 + 32 𝑥 + 43 𝑥 + 54 𝑥 + 3 𝑥 + 4 𝑥 + 5 2 𝑥2+4𝑥+5𝑥+20+3 𝑥2+3𝑥+5𝑥+15+ 4 𝑥2+3𝑥+4𝑥+12 𝑑𝑦𝑑𝑥 = 𝑥 + 32 𝑥 + 42 𝑥 + 53 2 𝑥2+9𝑥+20+3 𝑥2+8𝑥+15+4 𝑥2+7𝑥+12 𝑑𝑦𝑑𝑥 = 𝑥 + 32 𝑥 + 42 𝑥 + 53 2 𝑥2+18𝑥+40+3 𝑥2+24𝑥+45+4 𝑥2+28𝑥+48 𝑑𝑦𝑑𝑥 = 𝑥 + 32 𝑥 + 42 𝑥 + 53 2 𝑥2+3 𝑥2+4 𝑥218𝑥+24𝑥+28𝑥+40+45+48 𝒅𝒚𝒅𝒙 = 𝒙 + 𝟑𝟐 𝒙 + 𝟒𝟐 𝒙 + 𝟓𝟑 𝟗 𝒙𝟐+𝟕𝟎𝒙+𝟏𝟑𝟑
Ex 5.5
Ex 5.5, 2
Ex 5.5, 3 Important
Ex 5.5, 4
Ex 5.5, 5 You are here
Ex 5.5,6 Important
Ex 5.5, 7 Important
Ex 5.5, 8
Ex 5.5, 9 Important
Ex 5.5, 10 Important
Ex 5.5, 11 Important
Ex 5.5, 12
Ex 5.5, 13
Ex 5.5, 14 Important
Ex 5.5, 15
Ex 5.5, 16 Important
Ex 5.5, 17 Important
Ex 5.5, 18
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