part 1 of 3 the function f(x) = sin(4ln x) is a composition, and so we must use the chain rule…

part 1 of 3 the function f(x) = sin(4ln x) is a composition, and so we must use the chain rule d/dxg(h(x))=g(h(x))h(x) to find its derivative. the \inside\ function is 4ln x and the \outside\ function is your answer cannot be understood or graded. more information. submit skip (you cannot come back)

part 1 of 3 the function f(x) = sin(4ln x) is a composition, and so we must use the chain rule d/dxg(h(x))=g(h(x))h(x) to find its derivative. the \inside\ function is 4ln x and the \outside\ function is your answer cannot be understood or graded. more information. submit skip (you cannot come back)

Answer

Explanation:

Step1: Identify composition structure

The function $y = f(x)=\sin(4\ln x)$ is of the form $y = g(h(x))$ where $h(x)=4\ln x$ and $g(u)=\sin(u)$.

Step2: Determine outside - function

The outside - function takes the result of the inside - function as its input. Here, when we consider the operation on $4\ln x$, the operation is taking the sine of it. So the outside function is $\sin(u)$ (where $u = 4\ln x$).

Answer:

$\sin(u)$ (or $\sin$ function with input $u$ where $u = 4\ln x$)