Partial Derivatives of e^(-ET) with Functions E and T: How to Solve"

steve0606
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Homework Statement




Find all first and second partial derivatives of the following function:

z = e^(-ET) where E and T are functions of z.

I know how to do partial differentiation, but not when the variables are functions of z? I don't understand - is there some sort of implicit partial differentiation?



Homework Equations





The Attempt at a Solution


I have no idea at how to start!
 
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steve0606 said:

Homework Statement




Find all first and second partial derivatives of the following function:
With respect to what variables?

z = e^(-ET) where E and T are functions of z.

I know how to do partial differentiation, but not when the variables are functions of z? I don't understand - is there some sort of implicit partial differentiation?



Homework Equations





The Attempt at a Solution


I have no idea at how to start!
 
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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