Question 20 - NCERT Exemplar - MCQs - Chapter 5 Class 12 Continuity and Differentiability

Last updated at April 16, 2024 by

If  y = √(sin⁡γ€–x+yγ€— ), then dy/dx is equal to

(A) cos⁡x/(2y-1) 

(B) cos⁡x/(1-2y)

(C) sin⁡x/(1-2y) 

(D) (-4x 3 )/(2y -1)

This question is similar to Example 25 - Chapter 5 Class 12 - Continuity and Differentiability

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Transcript

Question 20 If y = √(sin⁑〖π‘₯+𝑦〗 ), then 𝑑𝑦/𝑑π‘₯ is equal to (A) cos⁑π‘₯/(2π‘¦βˆ’1) (B) cos⁑π‘₯/(1βˆ’2𝑦) (C) sin⁑π‘₯/(1βˆ’2𝑦) (D) (βˆ’4π‘₯^3)/(2𝑦 βˆ’1) 𝑦=√(𝑠𝑖𝑛⁑〖π‘₯+𝑦〗 ) Squaring both sides 𝑦^2=(√(sin⁑〖π‘₯+𝑦〗 ))^2 π’š^𝟐=π’”π’Šπ’β‘γ€–π’™+π’šγ€— 𝑦^2βˆ’π‘¦=sin⁑π‘₯ Differentiating both sides wrt π‘₯ (𝑑〖(𝑦〗^2))/𝑑π‘₯βˆ’π‘‘π‘¦/𝑑π‘₯ = (𝑑(𝑠𝑖𝑛⁑〖π‘₯)γ€—)/𝑑π‘₯ πŸπ’š π’…π’š/π’…π’™βˆ’π‘‘π‘¦/𝑑π‘₯=𝒄𝒐𝒔⁑𝒙 𝑑𝑦/𝑑π‘₯(2yβˆ’1) =π‘π‘œπ‘ β‘π‘₯ π’…π’š/𝒅𝒙 = 𝒄𝒐𝒔⁑𝒙/((πŸπ’š βˆ’ 𝟏)) So, the correct answer is (A)

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.