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Problem 7 Easy Difficulty

Determine the equation of the tangent to the curve defined by $y=x e^{-x}$ at the point $A\left(1, e^{-1}\right)$.

Answer

$y=\frac{1}{e}$

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{'transcript': "he It's clear. So when you right here. So our first gonna differentiate using the quotient role. So we have tea. Why? Over t x is equal to one plus each The x the derivative of one plus X minus one plus eat x The derivative times one plus x This is all over one plus Eat the X square. This is equal to one plus eat the X times one minus Eat the x one plus X All over one plus Eat the X square. This becomes equal to one minus x Eat the X over one plus each the X square and to find the slope of the 10 gents, we're gonna plug in zero when we get 1/4 and the equation becomes why minus one have equals 1/4 times X minus zero and this becomes equal to x over four plus 1/2"}