Question

Let $f\left(x\right)$ be an odd function. Then $f^{\prime }\left(x\right)$ is

• A. is an even function
• B. is an odd function
• C. may be even or odd
• D. neither even nor odd

Answer 1

The correct option is A is an even function

If $f\left(x\right)$ is and odd function, then
$f\left(x\right)+f(-x)=0$
Differentiating the above expression with respect to x, gives us
$f^{\prime }\left(x\right)-f^{\prime }(-x)=0$
Or
$f^{\prime }\left(x\right)=f^{\prime }(-x)$
Hence $f^{\prime }\left(x\right)$ is an even function.