The discussion revolves around simplifying and applying exponent rules in the context of differentiation, specifically involving a function expressed with multiple layers of exponents and roots.
Participants are actively exploring the simplification of the expression and have identified a potential simplification. Some guidance has been provided regarding the differentiation process, and there is an acknowledgment of the challenges posed by the exponents.
There is a focus on the correct handling of exponents and roots, with participants questioning their assumptions about the expression's structure. No explicit consensus has been reached, but there is progress in understanding the simplification process.
Although you can't tell from the above, from your work below, it appears that the radical is a cube root.Torshi said:Homework Statement
([3√(x^2+4)^4]^2
Torshi said:Homework Equations
None needed.
Chain rule
product rule etc
The Attempt at a Solution
I stopped at:
[((x^2+4)^4)^1/3]^2
So I have 3 exponents. I don't know how to simplify this in order to move on to do the chain rule or whatever rule that comes next. The exponents are killing me
Mark44 said:Although you can't tell from the above, from your work below, it appears that the radical is a cube root.
Is this what you're trying to differentiate?
## (\sqrt[3]{(x^2 + 4)^4})^2##What does (ar)s simplify to?
Mark44 said:OK, that's the first step.
Now, what is d/dx[(x2 + 4)8/3]?