If f(x) is an even function and f^{prime}(x) | vedclass

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(B) Given that $f(x)$ is an even function,we have $f(-x) = f(x)$.Differentiating both sides with respect to $x$,we get $f^{\prime}(-x) \cdot (-1) = f^

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(B) Given that $f(x)$ is an even function,we have $f(-x) = f(x)$.Differentiating both sides with respect to $x$,we get $f^{\prime}(-x) \cdot (-1) = f^{\prime}(x)$.This implies $f^{\prime}(-x) = -f^{\prime}(x)$,which means $f^{\prime}(x)$ is an odd function.Substituting $x = e$,we get $f^{\prime}(-e) = -f^{\prime}(e)$.Therefore,$f^{\prime}(e) + f^{\prime}(-e) = f^{\prime}(e) - f^{\prime}(e) = 0$.

If $f(x)$ is an even function and $f^{\prime}(x)$ exists,then $f^{\prime}(e) + f^{\prime}(-e)$ is

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