Question

The derivative of an even function is always

• A. an odd function
• B. an even function
• C. does not exist
• D. none of these

Answer 1

Answer: (A)

Since f is even $\therefore f(-x)=f(x)$
$\therefore f^{\prime }(-x)(-1)=f^{\prime }(x)\Rightarrow f^{\prime }(-x)=-f^{\prime }(x)$
$\therefore f^{\prime }$ is an odd function.