Differentiate the following

Question

y= e^-2x cos6x

y= -9(sin^2)x / cosx

Answer 1

y = e^-2xcos(6x)

dy/dx = (e^-2x)'cos(6x) + e^-2xcos(6x)' <-- Product Rule

dy/dx = -2e^-2xcos(6x) - 6e^-2xsin(6x)

y = -9sin²(x)/cos(x)

y = -9sin(x)[sin(x)/cos(x)]

y = -9sin(x)tan(x) <-- Simplified

dy/dx = -9cos(x)tan(x) + [-9sin(x)sec²(x)] <-- Product Rule

dy/dx = -9sin(x) - 9tan(x)sec(x)

Hope this helped!