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Class 12 Continuity And Differentiability · Mcq Single Correct1 Marksimplicit_differentiation

Class 12 Maths · Continuity And Differentiability · Mcq Single Correct #19

If tan((x+y)/(x−y))=k is constant, find dy/dx on a differentiable branch with x≠0,x≠y.

✅ Step-by-Step Solution

Final Answer: Option (B): y/x
  1. Differentiate the tangent relation locally: sec²u·u′=0 gives u′=0. Quotient differentiation yields (x−y)(1+y′)−(x+y)(1−y′)=0, hence 2xy′=2y.

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