Question

evaluate using product, chain, quotient sec(2theta)tan^2(theta)

Answer 1

fire!!
product rule hardcore... lol
f(x)g(x) = f'(x)g(x) + g'(x)f(x)
so...
derivative of sec(x) is x'sec(x)tan(x)
so ur first term is gonna be
2sec(2theta)tan(2theta) times g(x) which is tan²(theta)
ur second term is is g'(x)f(x)
so you use chain rule on tan²(theta) to get 2tan(theta)sec²(theta) times sec(2theta)
put it all together to get....
2sec(2x)tan(2x)tan²(x) + (2tan(x)sec²(x))(2sec(2x))
lol