Traditional Culture Encyclopedia - Travel guide - How to prove that the derivative function of differentiable odd function is even?

How to prove that the derivative function of differentiable odd function is even?

F (-x) =-f (x), both sides of the derivative, there are:

F'(-x)(-x)'=-F'(x)

-F'(-x)=-F'(x)

F'(-x)=F'(x)

That is to say, F'(x) is an even function.