AP Calc - Find a Derivative Formula

[bobraymund]

Homework Statement

If y = f(u) and u = g(x), where f and g possesses third derivatives, find a formula for

similar to the one below:

Homework Equations

The Attempt at a Solution

Ok, so I am basically completely lost on this one... because I came up with a solution for d^3y/d^3x, but not the way they want it which is d^3y/dx^3. I don't get how it can be the third derivative of y with respect to x cubed.

Perhaps I am making it more confusing, but can someone please clarify/explain?

Thanks,
Bob

 

[Dick]

It's not the third derivative with respect to x^3. It's just the third derivative with respect to x that they want. That's just sort of a funkyness about the d/d notation.
$$\frac{d^3 y}{dx^3}$$
just means the third derivative. Nothing to do with x cubed. It's just the way they write it.

 

[bobraymund]

It's not the third derivative with respect to x^3. It's just the third derivative with respect to x that they want. That's just sort of a funkyness about the d/d notation.
$$\frac{d^3 y}{dx^3}$$
just means the third derivative. Nothing to do with x cubed. It's just the way they write it.

Thanks a bunch for the clarification. I think I got the right answer now. :)

-Bob