If f(x) is an even function, then write whether f’ (x) is even or odd.
f(x) is an even 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 odd function. (Ans)