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If f(x) is an even function, then f′(x) is

If f(x) is an even function, then f′(x) is Correct Answer is odd function.

Concept:

If f(x) is an even function, then f(-x) = f(x)

If f(x) is odd function, then f(-x) = -f(x)

Calculation:

If f(x) is an even function, then

f(-x) = f(x)

Differentiating with respect to x, we get

⇒ -f′(-x) = f′(x)

⇒ f′(-x) = -f′(x)

Hence f′(x) is odd function.

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