How do I find the solution to this derivative problem?

  • Thread starter Thread starter Cuisine123
  • Start date Start date
  • Tags Tags
    Derivative
Click For Summary

Homework Help Overview

The problem involves finding the derivative of the function (1/g^2) at a specific point, given values for two functions f and g and their derivatives at that point. The subject area pertains to calculus, specifically the application of derivative rules.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the application of the quotient and product rules and question how to approach the derivative of (1/g^2). There is a focus on whether the chain rule has been learned and its relevance to the problem.

Discussion Status

Some participants have provided hints regarding the use of the chain rule and the derivative of (1/g^2). There is an ongoing exploration of the correct expression for the derivative, with attempts to evaluate it at the specified point.

Contextual Notes

There is an indication that the original poster may not have complete familiarity with the necessary derivative rules, and there are suggestions to clarify notation in the context of multiplication.

Cuisine123
Messages
38
Reaction score
0

Homework Statement


Two functions f and g are such that f(4)=3, f prime (4)= -2, g(4)=7, and g prime (4)=5. Determine (1/g^2) prime(4). By "prime" I mean when there is something that looks like a little "1" exponent on the letter.

Please help and give clear step by step explanations. Thanks.


Homework Equations


N/A


The Attempt at a Solution


I know what is the quotient and product rules are, but I have no idea how to approach this question.
 
Physics news on Phys.org
Have you learned the chain rule yet?

My hint is: what is the derivative of
\frac{1}{[g(x)]^2}?
 
n!kofeyn said:
Have you learned the chain rule yet?

My hint is: what is the derivative of
\frac{1}{[g(x)]^2}?

Is it -2g(x)^-3 x g(x)?
 
Hint #2:
Chain rule: f(g(x)) = f'(g(x))g'(x)

In this case...
f(g(x)) = g(x)^-2

Soooo...
 
Cuisine123 said:
Is it -2g(x)^-3 x g(x)?

Exactly. Now evaluate your expression at x=4.

Also, don't use x for multiplication. * would work better. :)
 

Similar threads

  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 11 ·
Replies
11
Views
2K
  • · Replies 16 ·
Replies
16
Views
3K
  • · Replies 6 ·
Replies
6
Views
1K
  • · Replies 24 ·
Replies
24
Views
3K
  • · Replies 2 ·
Replies
2
Views
1K
Replies
2
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K