# Hard Derivative

1. Feb 6, 2013

### Torshi

1. The problem statement, all variables and given/known data

([3√(x^2+4)^4]^2

2. Relevant equations

None needed.
Chain rule
product rule etc

3. 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

2. Feb 6, 2013

### Staff: Mentor

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?

3. Feb 6, 2013

### Torshi

I think it simplified down to (x^2+4)^8/3
I multiplied the exponents: 1/3 * 4/1 * 2/1 = 8/3

4. Feb 6, 2013

### Staff: Mentor

OK, that's the first step.

Now, what is d/dx[(x2 + 4)8/3]?

5. Feb 7, 2013

### Torshi

I figured it out. Thank you. My main issue was with the exponents in regards to if I had to multiply all of them together which was true.

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