Question 12 - CBSE Class 12 Sample Paper for 2022 Boards (MCQ Based - for Term 1) - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at August 14, 2026 by Teachoo

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)

Ques 12 (MCQ) - If e^x + e^y = e^(x+y) , then 𝑑𝑦/𝑑𝑥 is: - Teachoo - CBSE Class 12 Sample Paper for 2022 Boards (MCQ Based - for Term 1)

part 2 - Question 12 - CBSE Class 12 Sample Paper for 2022 Boards (MCQ Based - for Term 1) - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards - Class 12

part 3 - Question 12 - CBSE Class 12 Sample Paper for 2022 Boards (MCQ Based - for Term 1) - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards - Class 12

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Transcript

Question 12 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) Given 𝑒^𝑥+𝑒^𝑦=𝑒^(𝑥 + 𝑦) 𝑒^𝑥+𝑒^𝑦=𝑒^𝑥.𝑒^𝑦 Dividing by 𝒆^𝒙.𝒆^𝒚 both sides 𝒆^𝒙/(𝒆^𝒙 𝒆^𝒚 )+𝒆^𝒚/(𝒆^𝒙 𝒆^𝒚 )=(𝒆^𝒙 𝒆^𝒚)/(𝒆^𝒙 𝒆^𝒚 ) 1/𝑒^𝑦 +1/𝑒^𝑥 =1 𝒆^(−𝒚)+𝒆^(−𝒙)=𝟏 Differentiating both sides w.r.t x 𝒅(𝒆^(−𝒚) )/𝒅𝒙+𝒅(𝒆^(−𝒙) )/𝒅𝒙=𝒅(𝟏)/𝒅𝒙 𝒆^(−𝒚).(𝒅(−𝒚))/𝒅𝒙−𝒆^(−𝒙)=𝟎 −𝑒^(−𝑦).𝑑𝑦/𝑑𝑥−𝑒^(−𝑥)=0 −𝑒^(−𝑦).𝑑𝑦/𝑑𝑥=𝑒^(−𝑥) 𝒅𝒚/𝒅𝒙=𝒆^(−𝒙)/(−𝒆^(−𝒚) ) 𝑑𝑦/𝑑𝑥=−𝑒^(−𝑥−(−𝑦)) 𝑑𝑦/𝑑𝑥=−𝑒^(−𝑥 + 𝑦) 𝒅𝒚/𝒅𝒙=−𝒆^(𝒚 − 𝒙) So, the correct answer is (c)

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