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

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

Derivatives

Differentiation

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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.

Derivatives

Differentiation

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