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)


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