Problem

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

Solution

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

From Solvely APP
Source: https://solvelyapp.com/problems/8616/

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