Question 22 - NCERT Exemplar - MCQs - Chapter 5 Class 12 Continuity and Differentiability (Term 1)

Last updated at Nov. 18, 2021 by Teachoo

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IfΒ y = β(sinβ‘γx+yγ ), then dy/dx is equal to

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Question 22
If y = β(sinβ‘γπ₯+π¦γ ), then ππ¦/ππ₯ is equal to
(A) cosβ‘π₯/(2π¦β1) (B) cosβ‘π₯/(1β2π¦)
(C) sinβ‘π₯/(1β2π¦) (D) (β4π₯^3)/(2π¦ β1)
π¦=β(π ππβ‘γπ₯+π¦γ )
Squaring both sides
π¦^2=(β(sinβ‘γπ₯+π¦γ ))^2
π^π=πππβ‘γπ+πγ
π¦^2βπ¦=sinβ‘π₯
Differentiating both sides wrt π₯
(πγ(π¦γ^2))/ππ₯βππ¦/ππ₯ = (π(π ππβ‘γπ₯)γ)/ππ₯
ππ π π/π πβππ¦/ππ₯=πππβ‘π
ππ¦/ππ₯(2yβ1) =πππ β‘π₯
π π/π π = πππβ‘π/((ππ β π))
So, the correct answer is (A)

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