Find an equation of the tangent line to the graph of $y = e^{- x^{2}}$ at the point $(5, \frac{1}{e^{25}})$ .
$y =$

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Answer

$y - \frac{1}{e^{25}} = - 10 e^{- 25} (x - 5)$

Steps

Step 1 ：Find the derivative of the function using the chain rule: $\frac{d y}{d x} = - 2 x e^{- x^{2}}$

Step 2 ：Find the slope of the tangent line at the point $(5, \frac{1}{e^{25}})$ by plugging in $x = 5$ into the derivative: $m = - 10 e^{- 25}$

Step 3 ：Use the point-slope form of a line to find the equation of the tangent line: $y - \frac{1}{e^{25}} = - 10 e^{- 25} (x - 5)$

Step 4 ： $y - \frac{1}{e^{25}} = - 10 e^{- 25} (x - 5)$