Need help with a derivative solution

  • Context: Undergrad 
  • Thread starter Thread starter Dyatlov
  • Start date Start date
  • Tags Tags
    Derivative
Click For Summary

Discussion Overview

The discussion revolves around the differentiation of a function with respect to a variable substitution, specifically how to show that d F(x)/dx = (1/a) (dF/du) when substituting x = au. The scope includes mathematical reasoning related to derivatives and variable substitution.

Discussion Character

  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • One participant asks how to demonstrate the relationship between the derivatives after substituting x = au.
  • Another participant suggests taking the derivatives of both sides and considering constants during the substitution process.
  • A participant expresses confusion after performing calculations, presenting an equation that appears to mix derivatives incorrectly.
  • A later reply emphasizes the importance of noting that dx = a·du in the context of the substitution.

Areas of Agreement / Disagreement

Participants do not reach a consensus, as confusion remains regarding the correct application of derivatives and the implications of the substitution.

Contextual Notes

There are unresolved mathematical steps and potential misunderstandings about the differentiation process and the treatment of constants in the context of the substitution.

Dyatlov
Messages
25
Reaction score
1
Hello.
We have the derivative of a function: d F(x)/dx. If we substitute x = au, how can I show that d F(x)/dx = (1/a) (dF/du) ?
 
Physics news on Phys.org
Dyatlov said:
Hello.
We have the derivative of a function: d F(x)/dx. If we substitute x = au, how can I show that d F(x)/dx = (1/a) (dF/du) ?

When you do a substitution, you take the derivatives of both sides (hint: take into account what is constant and what is not). If you do this, you'll immediately come to what you need to show.
 
Thanks for the answer, did it and got:
(dF/da) (dF/du) = (dF/da) u + (dF/du) a = (dF/du) a, since a is a constant. What am I missing here?
 
Dyatlov said:
Thanks for the answer, did it and got:
(dF/da) (dF/du) = (dF/da) u + (dF/du) a = (dF/du) a, since a is a constant. What am I missing here?

As I previously said, note that ##dx = a\cdot du##.
 
  • Like
Likes   Reactions: Dyatlov
Thanks, got it now.
 
  • Like
Likes   Reactions: QuantumQuest

Similar threads

Undergrad A question about variables of integration
  • · Replies 3 ·
Replies
3
Views
7K
Undergrad 2nd order ODE's, variation of parameters and the notorious constraint
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Why Lagrange’s method of solving Pp + Qq=R works?
  • · Replies 3 ·
Replies
3
Views
1K
Graduate Solve the Partial differential equation ##U_{xy}=0##
  • · Replies 3 ·
Replies
3
Views
4K
Undergrad Understanding the Chain Rule in Derivatives: An Analysis of MIT Lecture Video
  • · Replies 9 ·
Replies
9
Views
2K
Undergrad Is it possible to solve such a differential equation?
  • · Replies 20 ·
Replies
20
Views
3K
Undergrad Finding Max and Min Extremes of a Function with Second Derivatives Equal to Zero
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Do these two partial derivatives equal each other?
  • · Replies 4 ·
Replies
4
Views
3K
Insights The Amazing Relationship Between Integration And Euler’s Number
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad FEM 2D Node Equations: Setting Up & Examples
  • · Replies 9 ·
Replies
9
Views
3K