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

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

Slide31.JPG

Slide32.JPG
Slide33.JPG

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

Transcript

Question 12 if 𝑒^π‘₯+ 𝑒^𝑦=𝑒^(π‘₯+𝑦), π‘‘β„Žπ‘’π‘› 𝑑𝑦/𝑑π‘₯ is : (a) 𝑒^(π‘¦βˆ’π‘₯) (b) 𝑒^(π‘₯+𝑦) (c) γ€–βˆ’π‘’γ€—^(π‘¦βˆ’π‘₯) (d) 2 𝑒^(π‘₯βˆ’π‘¦) Given 𝑒^π‘₯+𝑒^𝑦=𝑒^(π‘₯ + 𝑦) 𝑒^π‘₯+𝑒^𝑦=𝑒^π‘₯.𝑒^𝑦 Dividing by 𝒆^𝒙.𝒆^π’š both sides 𝒆^𝒙/(𝒆^𝒙 𝒆^π’š )+𝒆^π’š/(𝒆^𝒙 𝒆^π’š )=(𝒆^𝒙 𝒆^π’š)/(𝒆^𝒙 𝒆^π’š ) 1/𝑒^𝑦 +1/𝑒^π‘₯ =1 𝒆^(βˆ’π’š)+𝒆^(βˆ’π’™)=𝟏 Differentiating both sides w.r.t x 𝒅(𝒆^(βˆ’π’š) )/𝒅𝒙+𝒅(𝒆^(βˆ’π’™) )/𝒅𝒙=𝒅(𝟏)/𝒅𝒙 𝒆^(βˆ’π’š).(𝒅(βˆ’π’š))/π’…π’™βˆ’π’†^(βˆ’π’™)=𝟎 βˆ’π‘’^(βˆ’π‘¦).𝑑𝑦/𝑑π‘₯βˆ’π‘’^(βˆ’π‘₯)=0 βˆ’π‘’^(βˆ’π‘¦).𝑑𝑦/𝑑π‘₯=𝑒^(βˆ’π‘₯) π’…π’š/𝒅𝒙=𝒆^(βˆ’π’™)/(βˆ’π’†^(βˆ’π’š) ) 𝑑𝑦/𝑑π‘₯=βˆ’π‘’^(βˆ’π‘₯βˆ’(βˆ’π‘¦)) 𝑑𝑦/𝑑π‘₯=βˆ’π‘’^(βˆ’π‘₯ + 𝑦) π’…π’š/𝒅𝒙=βˆ’π’†^(π’š βˆ’ 𝒙) So, the correct answer is (c)

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

About the Author

Davneet Singh's photo - Teacher, Engineer, Marketer
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.