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

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

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

Answer»

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.

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