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AP EAMCET2006MathematicsFunctions

f(x)=e^x x , then f^ (6) (x) is equal to :

Options

  1. Ae^ 6 x 6 x
  2. B-8 e^x x
  3. C8 e^x x
  4. D8 e^x x

Correct answer

B. -8 e^x x

Step-by-step solution

f(x)=e^x x f^ (x)=e^x x+ x e^x f^ (x)=e^x x-e^x x+e^x x+e^x x=2 e^x x Now, f^ (x)=-2 e^x x+2 e^x x and f^ i v (x)=-2 e^x x-2 e^x x+2 e^x x-2 e^x x=-4 e^x xf^v(x)=-4 e^x x-4 e^x xf^ v i (x)=-4 e^x x+4 e^x x+4 e^x x-4 e^x x=-8 e^x x

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