differentiate f(x)=Tan^3(e^2x +1)

Answer 1

Let v(x) = e^2x + 1
dv/dx= 2 e^2x
Let u(v) = tan^3 v

f(x) = u[(v(x)]
df/dx = du/dv * dv/dx

For du/dv, let f(g) = g^3 and
g(v) = tan v

u = f{g(v)}
du/dv = df/dg * dg/dv = 3 g^2 * sec^2(v)
= 3 tan^2v*sec^2(v)

df/dx= 2e^(2x)*3tan^2v*sec^2(v)

Substitute e^2x +1 for v for the derivative imn terms of x.