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99 Percentile Qs Bank for JEE MainMathematicsDifferentiation

If ( cos   x ) y = ( sin y ) x ,   find   d y d x .

Options

  1. Alog cos y + y tan x log cos x − x cot y
  2. Blog sin y + y tan x log cos x − x cot y
  3. Clog sin y − y tan x log cos x + x cot y
  4. Dlog sin y + y tan x log sin x − x cot y

Correct answer

B. log sin y + y tan x log cos x − x cot y

Step-by-step solution

We have, ( cos x ) y = ( sin y ) x Taking logarithms on both sides, we get y   log   cos x = x log sin y Differentiate with respect to x we get y   log   cos x = x log sin y

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