Find the outside and inside functions of the following to find their derivatives:

Question

1) sqrt(2x+9)

2) cos(cos(x))

3) tan(x)

I already know how to find their derivatives I'm just not exactly sure what parts of the chain rule equation would be considered the outside and inside.

Answer 1

The chain rule says that if we have u(x) and f(u(x)),

df/dx = df/du * du/dx

f is the outside function, u is the inside.

So, in the first case
f(u) = √u
u(x) = 2x+9

#2.
f(u) = cos(u)
u(x) = cos(x)

#3. Is almost a trick question.
f(u) = tan(u)
u(x) = x