differentiate y = tan^2(3x) + sec^2(3x)

Answer 1

Use the chain rule separately for each of the two terms. The first term can be differentiated as follows:

Let u = tan 3x and v = u^2
tan^2(3x) = v{u(x)}

d/dx [tan^2(3x)] = (dv/du)*(du/dx)
= 2u * 3 sec^2 3x
= 6 tan(3x)*sec^2(3x)

Use a similar procedure to differentiate sec^2(3x)