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AP EAMCET2005MathematicsDifferentiation

If f(x)=10 x+(13+2 x) x, then f^ (x)+f(x) is equal to

Options

  1. Ax
  2. B4 x
  3. Cx
  4. D4 x

Correct answer

B. 4 x

Step-by-step solution

Given that On differentiating w.r.t. x , we get f^ (x)=-10 x+(13+2 x) x+2 x Again differentiating, we get aligned f^ (x)=-10 x-(13+2 x) x+ & 2 x & +2 x ...(ii) aligned On adding Eqs. (i) and (ii), we get f^ (x)+f(x)=2 x+2 x=4 x

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