What is the first derivative of y=tan^4(x+1)^4 ?

To find the first derivative of
tan^4x(x+1)^4.

Let f(x) ={
tan(x+1)^4}^4.

We know d/dx(tanx )=
sec^2x.

We know d/dx{f(x)}^n = n
{f(x)}^(n-1)*f'(x).

We know d/dx (u(v(x)) =
(d/dv){u(v(x)}{dv(x)/dx}.

Therefore d/dx{tan(x+1)^4}^4 =
d/dv(x(tanv)^4 * dv/dx, where v =
(x+1)^4.

d/dx{tan(x+1)^4}^4 = {4(tanv)^3sec^2v}
dv/dx.

d/dx{tan(x+1)^4}^4 = {4[tan(x+1)^4]^3sec^2 (x+1)^4}
d/dx(x+1)^4.

d/dx(tan(x+1)^4}^4 =
{4[tan(x+1)^4]^3sec^2(x+1)^4}{4(x+1)^3

Therefore
d/dx{tan(x+1)^4}^4 = 16(x+1)^3{[tan(x+1)^4]^3secx^2(x+1)^4}.