Find derivative of composite function

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Homework Help Overview

The discussion revolves around finding the derivative of a composite function, specifically the equation z=6x8ln(x), where both z and x are functions of t. The problem involves calculating dz/dt given a specific value of dx/dt.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the need to rearrange the equation and question the interpretation of the term "6x8." There is mention of applying the chain rule and revisiting the properties of logarithms, particularly ln(e).

Discussion Status

The discussion is active with participants seeking clarification on the equation's components and the application of relevant mathematical principles. Some guidance has been offered regarding the chain rule and logarithmic properties, but no consensus has been reached on the approach to take.

Contextual Notes

There appears to be confusion regarding the notation used in the equation, which may affect the understanding of the problem. Participants are also encouraged to revisit foundational concepts related to logarithms.

53Mark53
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Homework Statement


[/B]
Consider the equation z=6x8ln(x) where z and x are functions of t.If dx/dt=5 when x=e calculate dz/dt.

Homework Equations


[/B]
Do I have to rearrange the equation to do this?

The Attempt at a Solution

 
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Not sure what the 6x8 means. Is it 6 times 8? 6x8?
 
haruspex said:
Not sure what the 6x8 means. Is it 6 times 8? 6x8?

its 6x^8
 
53Mark53 said:

Homework Statement


[/B]
Consider the equation z=6x8ln(x) where z and x are functions of t.If dx/dt=5 when x=e calculate dz/dt.

Homework Equations


[/B]
Do I have to rearrange the equation to do this?

The Attempt at a Solution


It is for problems like this one that the chain rule was invented.
 
At some point you will have to work out what (ln e) is. Possibly go back to basics and remind yourself what ln aka loge means.
 
Last edited:

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