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AP EAMCET2001MathematicsDifferentiation

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

Options

  1. A4 a
  2. B1 8 a
  3. C1 4 a
  4. D8 a

Correct answer

C. 1 4 a

Step-by-step solution

aligned & We have, f(x)= x^2 x+a & f^ (x)= 2 x x+a - x^2 (x+a)^2 & f^ (x)= 2 x+a - 2 x (x+a)^2 - 2 x (x+a)^2 + 2 x^2 (x+a)^3 & f^ (a)= 2 2 a - 2 a 4 a^2 - 2 a 4 a^2 + 2 a^2 8 a^3 & = 1 a - 1 2 a - 1 2 a + 1 4 a & = 1 a - 1 a + 1 4 a & = 1 4 a & aligned

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