If f(x) is an odd function, then write whether f’(x) is even or odd.
f(x) is an odd function.
This means that f(-x) = -f(x).
If we differentiate this equation on both sides w.r.t. x, we get –
f’(-x).(-1) = -f’(x)
or, f’(-x) = f’(x)
i.e., f’(x) is an even function. (Ans)