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If f(x) is an odd function, then writ...

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

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`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.
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