Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class

Ex 5.5

Ex 5.5, 1
Important

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

Last updated at May 29, 2023 by Teachoo

Ex 5.5, 5 Differentiate the functions in, (𝑥 + 3)^2 . (𝑥 + 4)^3 . (𝑥 + 5)^4 Let 𝑦= (𝑥 + 3)^2 . (𝑥 + 4)^3 . (𝑥 + 5)^4 Taking log both sides log𝑦 = log ((𝑥 + 3)^2 . (𝑥 + 4)^3 . (𝑥 + 5)^4 ) log𝑦 = log (𝑥 + 3)^2 + log (𝑥 + 4)^3 + log (𝑥 + 5)^4 log𝑦 = 2 log (𝑥 + 3) + 3 log (𝑥 + 4) + 4 log (𝑥 + 5) Differentiating both sides 𝑤.𝑟.𝑡.𝑥. 𝑑(log𝑦 )/𝑑𝑥 = (𝑑 (2 log (𝑥 + 3)" + " 3 log (𝑥 + 4)" + " 4 log (𝑥 + 5)))/𝑑𝑥 𝑑(log𝑦 )/𝑑𝑥 (𝑑𝑦/𝑑𝑦) = 𝑑(2 log (𝑥 + 3))/𝑑𝑥 + (𝑑 (3 log (𝑥 + 4)))/𝑑𝑥 + 𝑑(4 log (𝑥 + 5))/𝑑𝑥 𝑑(log𝑦 )/𝑑𝑦 (𝑑𝑦/𝑑𝑥) = 2 𝑑(log (𝑥 + 3))/𝑑𝑥 + 3 (𝑑 (log (𝑥 + 4)))/𝑑𝑥 + 4 𝑑(log (𝑥 + 5))/𝑑𝑥 1/𝑦 × 𝑑𝑦/𝑑𝑥 = 2. 1/((𝑥 + 3) ) . 𝑑(𝑥 + 3)/𝑑𝑥 + 3. 1/((𝑥 + 4) ) . 𝑑(𝑥 + 4)/𝑑𝑥 + 4. 1/((𝑥 + 5) ) . 𝑑(𝑥 + 5)/𝑑𝑥 1/𝑦 × 𝑑𝑦/𝑑𝑥 = 2/(𝑥 + 3) (𝑑𝑥/𝑑𝑥+𝑑(3)/𝑑𝑥) + 3/(𝑥 + 4) (𝑑𝑥/𝑑𝑥+𝑑(4)/𝑑𝑥) + 4/(𝑥 +5) (𝑑𝑥/𝑑𝑥+𝑑(5)/𝑑𝑥) 1/𝑦 × 𝑑𝑦/𝑑𝑥 = 2/(𝑥 + 3) (1+0) + 3/(𝑥 + 4) (1+0) + 4/(𝑥 + 5) (1+0) 1/𝑦 × 𝑑𝑦/𝑑𝑥 = 2/(𝑥 + 3) + 3/(𝑥 + 4) + 4/(𝑥 + 5) 𝑑𝑦/𝑑𝑥 = 𝑦 (2/(𝑥 + 3) " + " 3/(𝑥 + 4) " + " 4/(𝑥 + 5)) Putting value of 𝑦 𝑑𝑦/𝑑𝑥 = (𝑥 + 3)^2 . (𝑥 + 4)^3 . (𝑥 + 5)^(4 ) (2/((𝑥 + 3) ) "+ " 3/((𝑥 + 4) ) " + " 4/((𝑥 + 5) )) 𝑑𝑦/𝑑𝑥 = (𝑥 + 3)^2 (𝑥 + 4)^3 (𝑥 + 5)^(4 ) ((2(𝑥 + 4) (𝑥 + 5) + 3(𝑥 + 3) (𝑥 + 5) + 4(𝑥 + 3) (𝑥 + 4))/((𝑥 + 3) (𝑥 + 4) (𝑥 + 5) )) 𝑑𝑦/𝑑𝑥 = ((𝑥 + 3)^2 (𝑥 + 4)^3 〖 (𝑥 + 5)〗^(4 ))/((𝑥 + 3) (𝑥 + 4) (𝑥 + 5) ) (2(𝑥^2+4𝑥+5𝑥+20)+3(𝑥^2+3𝑥+5𝑥+15)+ 4(𝑥^2+3𝑥+4𝑥+12)) 𝑑𝑦/𝑑𝑥 =(𝑥 + 3) (𝑥 + 4)^2 〖 (𝑥 + 5)〗^(3 ) (2(𝑥^2+9𝑥+20)+3(𝑥^2+8𝑥+15)+4(𝑥^2+7𝑥+12)) 𝑑𝑦/𝑑𝑥 =(𝑥 + 3) (𝑥 + 4)^2 〖 (𝑥 + 5)〗^(3 ) (2𝑥^2+18𝑥+40+3𝑥^2+24𝑥+45+4𝑥^2+28𝑥+48) 𝑑𝑦/𝑑𝑥 =(𝑥 + 3) (𝑥 + 4)^2 〖 (𝑥 + 5)〗^(3 ) (2𝑥^2+3𝑥^2+4𝑥^2 18𝑥+24𝑥+28𝑥+40+45+48) 𝒅𝒚/𝒅𝒙 =(𝒙 + 𝟑) (𝒙 + 𝟒)^𝟐 〖 (𝒙 + 𝟓)〗^(𝟑 ) (𝟗𝒙^𝟐+𝟕𝟎𝒙+𝟏𝟑𝟑)