Write the composite function in the form f(g(x)). [Identify the inner function u = g(x) and the outer function y = f(u).]

Question

y=3 square root 1+7x

(g(x), f(u)) =

Find the derivative dy/dx.

dy/dx =

Answer 1

Let u = g(x) = 1+7x and f(x) = √x

Then y = f(g(x) = f(1+7x) = √u = √(1+7x)

dy/dx = (dy/du)(du/dx) = (1/2)u^-1/2(7) = 7/(2√u) = 7 / (2√(1+7x))