Position of Electron Moving Along x-Axis at Momentary Stop

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To determine the position of the electron when it momentarily stops, the equation x(t) = 18t e^(-2.5t) must be differentiated with respect to time. The derivative will help find the velocity, which is set to zero to identify the momentary stop. The discussion highlights the need to apply the product rule for differentiation, as the position function is a product of two functions: f(t) = 18t and g(t) = e^(-2.5t). Participants seek clarification on differentiating products and exponentials in this context. Ultimately, solving for the time when the velocity is zero will reveal the electron's position relative to the origin.
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A electron moving along the x-axis has a position given by x = 18 te-2.5 t m, where t is in seconds. How far is the electron from the origin when it momentarily stops?

I am pretty sure that I have to differentiate this equation, and find where it equals zero and solve, I guess the biggest problem that I am having is doing the differentiating, some help please.
 
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Is the equation x(t) = 18t e-2.5t?

Can one differentiate f(t)*g(t) and exponentials? Here f(t) = 18t and g(t) = e-2.5t
 
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