Simplify Derivative of log(x^2 + y^2) - z^3

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Homework Help Overview

The discussion revolves around simplifying the expression for the differential of the function log(x^2 + y^2) - z^3, which involves understanding the application of derivatives and differentials in multivariable calculus.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the interpretation of the variable 'd' in the context of the problem, with some suggesting it may not represent a derivative. There is uncertainty about how to handle the logarithmic term and whether substitution is appropriate. Others propose using partial derivatives to express the differential of the function.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem. Some guidance has been offered regarding the formulation of the differential, but no consensus has been reached on the approach to simplifying the expression.

Contextual Notes

There is a noted confusion regarding the notation used in the problem, particularly the use of 'd' and its implications for differentiation versus being treated as a variable. Participants are also considering the implications of working with a function of multiple variables.

mill
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Homework Statement



Simplify ##d(log(x^2 + y^2) − z^3)##

Homework Equations



the derivative?

The Attempt at a Solution



The instruction says to simplify. In a similar problem I ended up using the d(a(b-c))= da d(b-c). I am not sure how to deal with the log and only found formulas for ln. Could I just substitute the whole log term with another variable?
 
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mill said:

Homework Statement



Simplify ##d(log(x^2 + y^2) − z^3)##

Homework Equations



the derivative?

The Attempt at a Solution



The instruction says to simplify. In a similar problem I ended up using the d(a(b-c))= da d(b-c). I am not sure how to deal with the log and only found formulas for ln. Could I just substitute the whole log term with another variable?
d is not the derivative. Its a variable there.
 
adjacent said:
d is not the derivative. Its a variable there.

The instruction says to simplify the differential. So I assumed it was the derivative?
 
The differential of a function of more variables ##df(x,y,z) =\frac{\partial f}{\partial x}dx+\frac{\partial f}{\partial y}dy+\frac{\partial f}{\partial z}dz.##

Now ##f(x,y,z) = log(x^2 + y^2) − z^3##. Take the partial derivatives and write up the differential.

ehild
 

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