How do you get the derivative of this?

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Discussion Overview

The discussion revolves around finding the derivative of a function representing electric charge in a circuits class, specifically determining the current from the charge function q = 5te^(-10^(3) t) Coulombs. Participants explore the application of the product rule and the chain rule in calculus to derive the current i = dq/dt.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant outlines their approach to finding the derivative of q, using the product rule and chain rule, but encounters a "weird answer."
  • Another participant suggests that the current answer may simply need simplification and questions what the current answer looks like.
  • A third participant confirms the general approach is correct and provides clarification on the derivative of g, indicating a potential misunderstanding in the calculation.
  • Further clarification is provided regarding the correction needed in the calculation of g', suggesting it should be -10^3 e^(-10^3 t) instead of a different interpretation.
  • Another participant prompts for factoring out e^(-10^3 t) from the derived expression to potentially match the answer in the textbook.

Areas of Agreement / Disagreement

Participants generally agree on the approach to use the product rule and chain rule, but there is no consensus on the correctness of the initial calculations or the "weird answer" produced. The discussion remains unresolved regarding the final form of the derivative.

Contextual Notes

There are indications of potential typos or misunderstandings in the derivative calculations, particularly concerning the application of the chain rule and simplification steps. However, these issues are not fully resolved within the discussion.

GrifteR150
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This is for my Circuits class, I am supposed to find the current i.

If q = 5te^(-10^(3) t) Coulombs


Find i (current) the formula for i is: i = dq/dt


So what I did was try to find the derivative of q, which is dq


So I brought out the constant 5, and I am left with te^(-10^(3) t)

and I recognize this as a product of two functions so I tried the product rule.


I let my first function f = t, and my second function g = e^(-10^(3) t)


so f ' = 1 and g ' (using the chain rule) i got (e^(-10^(3) t) x '10^3)



so i plugged it into the product role (fg)' = fg' + gf' and i get a weird answer.


The given answer in the back of the book is :

i = 5(1-10^3 t)e^(-10^3 t) Amps

can someone help me please
 
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Perhaps you just need to simplify? What does your current answer look like?

PS: we have a homework section :wink:
 
Your general approach is correct. g' = e^(-10^(3) t) * -10^3

When you plug this into the product rule, you get a "weird answer?" Are you sure that your weird answer is not, in fact, the correct answer in unsimplified form?

- Warren
 
It looks to me that if you make a small correction in your calculation of g', then you will get the same answer as the book.
 
GrifteR150 said:
This is for my Circuits class, I am supposed to find the current i.

If q = 5te^(-10^(3) t) Coulombs


Find i (current) the formula for i is: i = dq/dt


So what I did was try to find the derivative of q, which is dq


So I brought out the constant 5, and I am left with te^(-10^(3) t)

and I recognize this as a product of two functions so I tried the product rule.


I let my first function f = t, and my second function g = e^(-10^(3) t)


so f ' = 1 and g ' (using the chain rule) i got (e^(-10^(3) t) x '10^3)
I presume that is a typo and it should be (e^(-10^(3)t) x (-10^3)) not
'10^3.

so i plugged it into the product role (fg)' = fg' + gf' and i get a weird answer.
How weird? You just said [itex]f= t, g'= -10^3 e^{-10^3t}, g= e^{-10^3t}, f'= 1[/itex] so [itex]fg'+ f'g= -10^3 te^{-10^3t}+ e^{-10^t}[/itex]
What do you get if you factor [itex]e^{-10^3 t}[/itex] out of that?

The given answer in the back of the book is :

i = 5(1-10^3 t)e^(-10^3 t) Amps

can someone help me please
 
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