Find the derivative of the function f(x) = sin^2 (tan 4x)?

Answer 1

f(x) = sin^2 (tan 4x)?

we have to apply chain rule here to find derivative

f' (x) = 2 sin(tan 4x) d/dx(sin(tan4x))

= 2 sin(tan 4x)cos(tan4x) d/dx tan 4x

= 2 sin(tan4x) cos(tan 4x) 4sec² 4x

=8 sin(tan 4x) cos(tan 4x) sec² 4x