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Manipal MET2011MathematicsDifferentiation

If Z=f(x+a y)+ (x-a y) , then

Options

  1. AZ_ x x =Z_ y y
  2. BZ_ x x =a^2 Z_ y y
  3. CZ_ y y =a^2 Z_ x x
  4. DNone of these

Correct answer

C. Z_ y y =a^2 Z_ x x

Step-by-step solution

Given that, aligned Z & =f(x+a y)+ (x-a y) Z_x & =f^ (x+a y)+ (x-a y) Z_ x x & =f^ (x+a y)+ ^ (x-a y) aligned and Z_y=a f^ (x+a y)-a ^ (x-a y) z_ y y =a^2 f^ (x+a y)-a^2 ^ (x-a y) Hence, a^2 Z_ x x =Z_ y y

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