Chain Rule of a functional to an exponential

Click For Summary

Homework Help Overview

The discussion revolves around the differentiation of a function defined as an exponential of another function, specifically involving the chain rule. The original poster presents a problem involving the function G(x) = [f(x)]^α and seeks to find its derivative G'(x).

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to apply the chain rule to differentiate the function and presents their result. Some participants question the precision of the variable α, suggesting it should not equal zero.

Discussion Status

The discussion includes confirmation of the original poster's differentiation attempt, along with a note on the condition regarding α. There is an acknowledgment of the correctness of the approach, but no further consensus or resolution has been reached.

Contextual Notes

Participants are discussing the implications of the variable α in the context of the differentiation process, particularly its value and impact on the function.

BreathingGloom
Messages
8
Reaction score
0

Homework Statement


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

Find the expression for [itex]G'(x)[/itex]


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



[itex]G'(x) = a[f(x)]^{a-1} \cdot f'(x)[/itex]
 
Physics news on Phys.org
Functional to an exponential.. haha. Not exactly what I meant, but okay.
 
That's correct. If you are being precise α ≠ 0.
 
  • Like
Likes   Reactions: 1 person
Much appreciated!
 

Similar threads

  • · Replies 4 ·
Replies
4
Views
1K
Replies
2
Views
2K
Replies
2
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
Replies
3
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 15 ·
Replies
15
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K