Let f(x)=xx, x∉Z, ([·] denotes greatest integer function), then f^(')x is equal to

Correct answer: (B) x. We have, f(x)=xx ∴ x is an integer. ⇒fx=px ∵[x]=p ⇒f^(')x=p=x ∴ f^(')x=x

Q80 / 125 · BITSAT 2019 · Mathematics

Let $f (x) = x [x], x \notin Z$ , ( $[\cdot]$ denotes greatest integer function), then $f^{'} (x)$ is equal to

We have, $f (x) = x [x]$

$∴ [x]$ is an integer.

$\Rightarrow f (x) = p x [∵ [x] = p]$

$\Rightarrow f^{'} (x) = p = [x]$

$∴ f^{'} (x) = [x]$

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