Question

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

• A. An odd function
• B. An even function
• C. May be even or may be odd
• D. Nothing can be said

Answer 1

The correct option is A An odd function

If $f\left(x\right)$ is an even function

Then $f(-x)=f\left(x\right)$

Differentiate above equation both sides,

$f^{\prime }(-x)(-1)=f^{\prime }\left(x\right)$

$\Rightarrow f^{\prime }(-x)=-f^{\prime }\left(x\right)$

Hence $f^{\prime }\left(x\right)$ is an odd function