If r=5(cot t+2)/e^t, find dr/dt

Question

If r= 5(cot t + 2)/e^t, find dr/dt

Answer 1

r = 5(cot t + 2) / e^t

Using the Quotient Rule, dr/dt = 5{[e^t(-csc²t) - e^t(cot t + 2)]/e^2t}

= -5e^t(csc²t + cot t + 2) / e^2t

= -5(csc²t + cot t + 2) / e^t