Posted by **Giselle** on Thursday, October 9, 2008 at 5:49pm.

What does it mean to be be an inside or outside function?

for example:

tell which is the inside function and which is the outside:

f(x)=sin3x

- calculus -
**Damon**, Thursday, October 9, 2008 at 7:17pm
The idea is that

df (g(x) )/dx = df/dg * dg/dx

where f is the "outside function and g is the "inside" function

You do the outside function derivative first, then the inside function

so for your example we have

f ( g(x) ) = sin (g(x)) = sin ( 3x )

f (g) = sin g outside

g = 3x inside

so in your case

df/dg = cos g outside = cos 3x

dg/dx = 3 inside

so df/dx = cos g * 3

or 3 cos 3x

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