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

Question

Philoid · Accepted Answer

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)