Let f(x) = √(4x + 2), let g(x) = √(x), and let u = 4x + 2. Thus, f(x) = g(u)

Question

Let f(x) = √(4x + 2),

let g(x) = √(x),

and let u = 4x + 2.

Thus, f(x) = g(u)

u' = 4

g'(u) = ?

Note: use sqrt() for √ sign

Answer 1

d(g(u))/du=(1/2)u^-(1/2)

[d(g(u(x))]/dx=[d(g(u))/du]*[du/dx]=(1/2)u^(-1/2)*4,,,,,,,,,,,4=du/dx

=2*(4x+2)^(-1/2)

=2/√(4x+2)