Question

How do you find the derivative of y=tan^2(x^4)?

Answer 1

just the chain rule

y = u^2 where u = tan(v) and v = x^4
y' = 2u u'
y' = 2u sec^2(v) v'
= 2u sec^2(v) (4x^3)
= 8x^3 tan(x^4) sec^2(x^4)

and, as usual, you can massage trig functions in various ways.

Answer 2

dy/dx = 2tan (x^4) * sec^2 (x^4) * 4x^3