A function f satisfies the relation f(x) = f' | vedclass

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(C) Given the relation $f(x) = f''(x) + f'''(x) + f''''(x) + \dots \infty$. Taking the derivative of both sides with respect to $x$,we get $f'(x) = f'

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$5$

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(C) Given the relation $f(x) = f''(x) + f'''(x) + f''''(x) + \dots \infty$. Taking the derivative of both sides with respect to $x$,we get $f'(x) = f'''(x) + f''''(x) + f'''''(x) + \dots \infty$. Substituting this into the original equation,we observe that $f(x) = f''(x) + f'(x)$. Rearranging the terms,we get $f'(x) + f''(x) = f(x)$. Evaluating this at $x = 1$,we have $f'(1) + f''(1) = f(1)$. Since $f(1) = 5$,it follows that $f'(1) + f''(1) = 5$.

$A$ function $f$ satisfies the relation $f(x) = f''(x) + f'''(x) + \dots \infty$,where $f(x)$ is an infinitely differentiable function. If $f(1) = 5$,then the value of $f'(1) + f''(1)$ is equal to:

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