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NDA2019MathematicsDifferentiationActual

Paragraph: Consider the equation x^y=e^ x-y Question: What is d y d x at x=1 equal to ?

Options

  1. A0
  2. B1
  3. C2
  4. D4

Correct answer

A. 0

Step-by-step solution

aligned & x^y=e^ x-y & ( d y d x )_ x=1 =? & at x=1 ; x^y=e^ x-y & 1=e^ 1-y & y=1 & x^y=e^ x-y & y, x=x-y aligned On differentiating w.r.t. x . aligned & y 1 x =1-y^1- x y^1 & 1- y x =y^1(1+ x) & y^1= x-y x(1+ n x) & y^1 at x=1 & = 1-1 1(1+0) =0 aligned

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