The discussion focuses on finding the first and second partial derivatives of the function z = e^(-ET), where E and T are functions of z. Participants express confusion regarding the application of partial differentiation when the variables are dependent on z. The concept of implicit differentiation is introduced as a potential method to tackle this problem. Clear steps and examples are necessary to illustrate the process of differentiating functions with interdependent variables.
PREREQUISITESStudents studying multivariable calculus, educators teaching calculus concepts, and anyone seeking to deepen their understanding of partial derivatives in functions with interdependent variables.
With respect to what variables?steve0606 said: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!