Differentiate. g(t) = 6 sec t + 4 tan t

Answer 1

//Use the product rule for each part of the sum

d[6sec(t)]/dt = 6 * sec(t)tan(t) + 0 * sec(t) = 6sec(t)tan(t)

d[4tan(t)]/dt = 4 * sec²(t) + 0 * tan(t) = 4sec²(t)

//Then add them together and simplify

d[6sec(t) + 4tan(t)]/dt = 6sec(t)tan(t) + 4sec²(t) = 2sec(t) [3tan(t) + 2sec(t)]