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AP EAMCET201825 Apr 2018Morning ShiftMathematicsDifferentiationActual

If y = a sin x + ( 5 + 2 x ) cos x , then y ' ' + y =

Options

  1. A4 cos x
  2. B- 4 cos x
  3. C4 sin x
  4. D- 4 sin x

Correct answer

D. - 4 sin x

Step-by-step solution

Given: y = a sin x + ( 5 + 2 x ) cos x     . . i Differentiating w.r.t. x , we get y ' = a cos x + 2 cos x - 5 + 2 x sin x y ' = a + 2 cos x - 5 + 2 x sin x Again differentiating w.r.t. x , we get y ' ' = - a + 2 sin x - 5 + 2 x cos x - 2 sin x     . . . i i Adding i   &   i i , we get y ' ' + y = a sin x + ( 5 + 2 x ) cos x   - a + 2 sin x - 5 + 2 x cos x - 2 sin x   = - 4 sin x .

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