# UNIT 7: calculus to solve engineering problems

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#1
The same capacitor circuit is now charged up to 12V and the instantaneous voltage is v=12(1- e^-t/2)a) Differentiate v with respect to t to give an equation for dv/dt?
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4 weeks ago
#2
Chain rule.

d/dt(12) = 0 so you only have to worry about d/dt(-12e^(-t/2))

To rigorously explain it, I'd substitute u = -t/2 and apply the chain rule, but I can't be bothered so I'll just tell you that the derivative of e^f(x) = f'(x)e^f(x), so the derivative of -12e^(-t/2) is just 6e^(-t/2).
Last edited by Filthy Communist; 4 weeks ago
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