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NDA2026MathematicsDifferentiationActual

Passage: Let (e^y )^x-y=0 , where y is a function of x whose domain is (0,10] . Question: What is dy dx equal to ?

Options

  1. Ay 1-xy
  2. By 1+xy
  3. Cy^2 1-xy
  4. Dy^2 1+xy

Correct answer

C. y^2 1-xy

Step-by-step solution

Given equation is (e^y)^x - y = 0 e^ xy = y Taking natural logarithm on both sides: xy = (y) Differentiating both sides with respect to x : y + x dy dx = 1 y dy dx y = ( 1 y - x ) dy dx y = ( 1 - xy y ) dy dx dy dx = y^2 1 - xy

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