1. i = 10te^(-5t), at what instant of time is the current maximum? first I differentiated i, using the product rule. di/dt = (10e^(-5t)) (1-5) , thats what I got after simplifying, im pretty certain this is correct. My confusion comes in when taking natural logarithms. if ln(e(^1)) = 1 then ln(e(^-5t)) = -5t, im just not entirely sure what to do from here but I gave it a shot. 10ln 5t(1-5) = 0 ln (50t-250t) = 0** ln (50/250) = t. The answer in the book is di/dt = 0 when t=1/5. If anyone can clear any of that up for me Id be very grateful. I have just spotted a glaring error** the 10 should be taken as a power, not a product. so it should be ln((5t/25t)^10) = 0 how do I calculate t?