if e x + e y =e (x+y) , then dy/dx is :

(a) e (y-x)      (b) e (x+y)
(c) -e (y-x)     (d) 2 e (x-y)

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  1. Class 12
  2. Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Transcript

Question 12 if ๐‘’^๐‘ฅ+ ๐‘’^๐‘ฆ=๐‘’^(๐‘ฅ+๐‘ฆ), ๐‘กโ„Ž๐‘’๐‘› ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ is : (a) ๐‘’^(๐‘ฆโˆ’๐‘ฅ) (b) ๐‘’^(๐‘ฅ+๐‘ฆ) (c) ใ€–โˆ’๐‘’ใ€—^(๐‘ฆโˆ’๐‘ฅ) (d) 2 ๐‘’^(๐‘ฅโˆ’๐‘ฆ) Given ๐‘’^๐‘ฅ+๐‘’^๐‘ฆ=๐‘’^(๐‘ฅ + ๐‘ฆ) ๐‘’^๐‘ฅ+๐‘’^๐‘ฆ=๐‘’^๐‘ฅ.๐‘’^๐‘ฆ Dividing by ๐’†^๐’™.๐’†^๐’š both sides ๐’†^๐’™/(๐’†^๐’™ ๐’†^๐’š )+๐’†^๐’š/(๐’†^๐’™ ๐’†^๐’š )=(๐’†^๐’™ ๐’†^๐’š)/(๐’†^๐’™ ๐’†^๐’š ) 1/๐‘’^๐‘ฆ +1/๐‘’^๐‘ฅ =1 ๐’†^(โˆ’๐’š)+๐’†^(โˆ’๐’™)=๐Ÿ Differentiating both sides w.r.t x ๐’…(๐’†^(โˆ’๐’š) )/๐’…๐’™+๐’…(๐’†^(โˆ’๐’™) )/๐’…๐’™=๐’…(๐Ÿ)/๐’…๐’™ ๐’†^(โˆ’๐’š).(๐’…(โˆ’๐’š))/๐’…๐’™โˆ’๐’†^(โˆ’๐’™)=๐ŸŽ โˆ’๐‘’^(โˆ’๐‘ฆ).๐‘‘๐‘ฆ/๐‘‘๐‘ฅโˆ’๐‘’^(โˆ’๐‘ฅ)=0 โˆ’๐‘’^(โˆ’๐‘ฆ).๐‘‘๐‘ฆ/๐‘‘๐‘ฅ=๐‘’^(โˆ’๐‘ฅ) ๐’…๐’š/๐’…๐’™=๐’†^(โˆ’๐’™)/(โˆ’๐’†^(โˆ’๐’š) ) ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ=โˆ’๐‘’^(โˆ’๐‘ฅโˆ’(โˆ’๐‘ฆ)) ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ=โˆ’๐‘’^(โˆ’๐‘ฅ + ๐‘ฆ) ๐’…๐’š/๐’…๐’™=โˆ’๐’†^(๐’š โˆ’ ๐’™) So, the correct answer is (c)

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.