Position of Electron Moving Along x-Axis at Momentary Stop

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SUMMARY

The position of an electron moving along the x-axis is defined by the equation x(t) = 18t e-2.5t m. To determine the distance from the origin when the electron momentarily stops, one must differentiate this equation with respect to time t and find the critical points where the velocity equals zero. The differentiation involves applying the product rule to the functions f(t) = 18t and g(t) = e-2.5t. The solution to this differentiation will yield the time at which the electron stops and its corresponding position.

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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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