Question

Calc Help Please! Problem attached.

Answer 1

So basically youre just looking for an outer function and an inner function. (fog)x means we took one function g and plugged it into every x variable that was in f. So even visually, it makes sense that the inner part of a function would be g and the outer part would be a part of f.

So in this case the inner is pretty easy, its x + sin(x). Now like I mentioned, fog(x) means this x + sin(x) had to go into an x that was in f(x). SO that being said, it makes sense for f(x) to just be x^3. Because if f is x^3 and g is x + sin(x), then fog(x) is just what we have
(x+sin(x))^3.

Do you know how to do chain rule from there?

Answer 2

Well,
\[ f[g(x)]=[x+sin(x)]^3 \\
f(x)=x^3 \\
g(x)=x+sin(x) \]
Now by chain rule
\[ (f[g(x)])′=f′[g(x)] \cdot g′(x) \]

can do?
and... im so slow on mobile that im second hehe

Answer 3

Yeah, but its better than my explanation, lol.