Chain Rule of a functional to an exponential

BreathingGloom
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Homework Statement


Suppose f is differentiable on \mathbb R and \alpha is a real number. Let G(x) = [f(x)]^a

Find the expression for G'(x)


Homework Equations



I'm pretty sure that I got this one right, but I really want to double check and make sure.

The Attempt at a Solution



G'(x) = a[f(x)]^{a-1} \cdot f'(x)
 
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Functional to an exponential.. haha. Not exactly what I meant, but okay.
 
That's correct. If you are being precise α ≠ 0.
 
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Much appreciated!
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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