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If $f(x)$ is an even function and $f^{\prime}(x)$ exists, then $\mathrm{f}^{\prime}(\mathrm{e})+\mathrm{f}^{\prime}(-\mathrm{e})$ is
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Since, $f(x)$ is an even function, therefore $f^{\prime}(x)$ is an odd function.
$$
f^{\prime}(-e)=-f^{\prime}(e)
$$
$\therefore \quad \mathrm{f}^{\prime}(\mathrm{e})+\mathrm{f}^{\prime}(-\mathrm{e})=0$
$$
f^{\prime}(-e)=-f^{\prime}(e)
$$
$\therefore \quad \mathrm{f}^{\prime}(\mathrm{e})+\mathrm{f}^{\prime}(-\mathrm{e})=0$
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