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

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

Steps

Step 1 ：Find the derivative of the function using the chain rule: $\frac{dy}{dx} = -2xe^{-x^2}$

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: $m = -10e^{-25}$

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

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