Question

If `f(x)= sec 4 x` and `g(x) = 2 x`, how do you differentiate `f(g(x))` using the chain rule?

Answer 1

8 sec8x tan 8x

Explanation:

f(g(x)=sec4(2x) =sec 8x

Chain rule in simple words is that if z is a function of t and t is a function of x, the `dz/dx= dz/dt .dt/dx`. Inthis case

let g(x) = t= 2x, so f(g(x)= f(t)= sec4t
Hence `(d(sec4t))/dx= (df)/dt. dt/dx=(d(sec4t))/dt (d(2x))/dx`

`=4sec 4t tan4t (d(2x))/dx`

= 4 sec 4t tan 4t (2)

=8 sec8x tan 8x