Q65 / 160 · TS EAMCET 2012 · Mathematics

If $f(x)=\left(x^2-1\right)^7$, then $f^{(14)}(x)$ is equal to

  • A
    $0$
  • B
    $2 !$
  • C
    $7 !$
  • Correct answer
    D
    $14 !$

Solution

Given, $f(x)=\left(x^2-1\right)^7$ When we expand above expansion it will give one term of $x^{14}$ whose coefficient is 1 . $\therefore \quad f^{14}(x)=14 !$

Hence, the correct answer is option: 'D'.

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