Question

Let $f\left(x\right)$ be an even function , then $f^{\prime }\left(x\right)$

• A. is an even function
• B. is an odd function
• C. may be even or odd
• D. does not exist

Answer 1

Answer: (B)

is an odd function

$f\left(x\right)=f(-x)$ (property of even funition)
$f^{\prime }\left(x\right)=-f^{\prime }(-x)$
Its a property of odd function
so $f^{\prime }\left(x\right)$ is an odd function