1. Chapter 5 Class 12 Continuity and Differentiability
2. Serial order wise
3. Ex 5.7

Transcript

Ex 5.7, 15 If ๐ฆ= ใ500๐ใ^7๐ฅ+ ใ600๐ใ^(โ7๐ฅ), show that ๐2๐ฆ/๐๐ฅ2 = 49๐ฆ ๐ฆ= ใ500๐ใ^7๐ฅ+ ใ600๐ใ^(โ7๐ฅ) Differentiating ๐ค.๐.๐ก.๐ฅ ๐๐ฆ/๐๐ฅ = (๐(ใ500๐ใ^7๐ฅ "+" ใ600๐ใ^(โ7๐ฅ) " " ))/๐๐ฅ ๐๐ฆ/๐๐ฅ = (๐ (ใ500๐ใ^7๐ฅ))/๐๐ฅ + (๐ (ใ600๐ใ^(โ7๐ฅ)))/๐๐ฅ ๐๐ฆ/๐๐ฅ = 500 (๐ (๐^7๐ฅ))/๐๐ฅ + 600 (๐ (๐^(โ7๐ฅ)))/๐๐ฅ ๐๐ฆ/๐๐ฅ = 500 . ๐^7๐ฅ. (๐ (7๐ฅ))/๐๐ฅ + 600 . ๐^(โ7๐ฅ) . (๐ (โ7๐ฅ))/๐๐ฅ ๐๐ฆ/๐๐ฅ = 500 . ๐^7๐ฅ. 7 + 600 . ๐^(โ7๐ฅ) . (โ7) ๐๐ฆ/๐๐ฅ = 500 . 7 . ๐^7๐ฅ โ 600 . 7 . ๐^(โ7๐ฅ) Again Differentiating ๐ค.๐.๐ก.๐ฅ ๐/๐๐ฅ (๐๐ฆ/๐๐ฅ) = ๐(500 . 7 . ๐^7๐ฅ " โ" ใ 600 . 7 . ๐ใ^(โ7๐ฅ) )" " /๐๐ฅ (๐^2 ๐ฆ)/(๐๐ฅ^2 ) = ๐(500 ร 7 . ๐^7๐ฅ )/๐๐ฅ + ๐(ใ600 ร7๐ใ^(โ7๐ฅ) )" " /๐๐ฅ (๐^2 ๐ฆ)/(๐๐ฅ^2 ) = 500 ร 7 ๐(๐^7๐ฅ )/๐๐ฅ โ 600 ร 7 ๐(๐^(โ7๐ฅ) )/๐๐ฅ = 500 ร 7 ร ๐^7๐ฅ ๐(7๐ฅ)/๐๐ฅ โ 600 ร 7 ร ๐^(โ7๐ฅ) ๐(โ7๐ฅ)/๐๐ฅ = 500 ร 7 ร ๐^7๐ฅ. 7 โ 600 ร 7 ร ๐^(โ7๐ฅ) (โ7) = 500 ร 7 ร 7๐^7๐ฅ โ 600 ร 7 ร 7 ร ๐^(โ7๐ฅ) = 7 ร 7 (500ใ ๐ใ^7๐ฅ+600ใ ๐ใ^(โ7๐ฅ) ) = 49 (500ใ ๐ใ^7๐ฅ+600ใ ๐ใ^(โ7๐ฅ) ) = 49 ๐ฆ Hence proved .

Ex 5.7