Question

\Write the composite function in the form f(g(x)). [Identify the inner function u = g(x) and the outer function y = f(u).] (Use non-identity functions for f(u) and g(x).) y = et + 9 (f(u), g(x)) =

Y= 3√E^+9
Find the derivative dy/dx
dy/dx= _____

Answer 1

The composite function in the form f(g(x)) is y = e^(3√(x+9)). Here, the inner function is u = g(x) = x + 9, and the outer function is y = f(u) = e^(3√u).

To find the derivative dy/dx, we can use the chain rule.

dy/dx = dy/du * du/dx

dy/du = e^(3√u) * (3/2) * (1/sqrt(u)) = (3/2) * e^(3√u) / √u

du/dx = 1

Therefore,

dy/dx = dy/du * du/dx = (3/2) * e^(3√u) / √u

Substituting u = x + 9, we get:

dy/dx = (3/2) * e^(3√(x+9)) / √(x+9)