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Problem 45 Easy Difficulty

If $ f(x) = e^x g(x), $ where $ g(0) = 2 $ and $ g'(0) = 5, $ find $ f'(0). $

Answer

$f^{\prime}(0)=7$

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Video Transcript

Hey, it's Claire. So in your rain here. So we're first when he used a product rule to find the formula for the derivative of F in terms of G. So we have the derivative of this equal to the derivative of E to the X turns g of X, less eat the eggs, terms the derivative of G X, and this is equal to eat the x times g to the ex less e to the X times, the derivative of G events. And then we're gonna just plug in what we know. So we get thanks the derivative of f of zero, which is equal to e to the zero times two less e to the zero times five. There's just becomes, too. This just becomes by we act these two together and get seven.