Implicit Derivation. Approximation for $f(0.01)$?

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Let $y=f(x)$ be the function described implicitly by $$y\cos x = e^x \ln y + e - 1$$

Give an approximation for $f(0.01)$. You do not need to simplify your answer.

How to give an approximation here? I have solved for $y'$. Thanks.

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Hint: $$f(0.01)\approx f(0)+f'(0)(0.01-0)=...$$