Applications of Exponential & Log Function Derivatives

2. The charge across a capacitor at any time t is given by:

q = e^{-0.02t}(0.05cos 2t)

Find the current in the circuit.

Remember that i = dq/dt.

Use the Product Rule:

i = dq/dt = e^{-0.02t}(-0.05sin 2t)(2) + (-0.02e^{-0.02t}(0.05cos 2t)

i = -e^{-0.02t}(0.1sin 2t + 0.05 cos2t)