What is the derivative of y = tan (4θ)

First, note that d/dx tan(f(x)) = f'(x)sec²(f(x)). Hence,

dy/dθ = 4sec²(4θ)

I hope this helps!

y = tan(4θ)
dy/dθ = sec^2(4θ)*4θ/θ
= 4sec^2(4θ)