Finding the equation for the tangent line.

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Homework Help Overview

The discussion revolves around finding the equation for the tangent line to the function \(y = e^x \cos x\) at the point where \(x = 0\). Participants are exploring the process of differentiation and the application of the point-slope form of a line.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to find the tangent line by calculating the function value and its derivative at \(x = 0\). Some participants question the correctness of the derivative and the application of the point-slope form. Others suggest that the original poster may have overlooked the chain rule in their differentiation process.

Discussion Status

The discussion is ongoing, with participants providing feedback on the original poster's attempts. There is acknowledgment of mistakes in the derivative calculation, and some guidance has been offered regarding the need for a complete problem statement and proper differentiation techniques.

Contextual Notes

There is a mention of the need for a more complete problem statement to facilitate assistance. The original poster has expressed confusion regarding the slope calculation and the correct application of differentiation rules.

cd246
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Homework Statement


find the equation for the tangent line.
1. (e^x)(cos x) where x=0

Homework Equations


plugged 0 into the equation, (e^0)(cos 0) and got 1 for the y-coordinate. so I got the points(0,1). For the slope, I derived the equation into -(e^x)(sin x). then i plugged 0 in and got 0 for the slope.
I used point-slope form, y-1=0(x-0)

The Attempt at a Solution


y-1=0(x-0) or y=1.
but the answer says x-y+1=0
I believe the slope was suppose to be 1 and I got 0, what is the right way to get the slope?
 
Last edited:
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I doubt anyone will help you until you post a more complete problem statement.
 
Sorry, I'm not tracking what you are trying to do. Are you saying that you have the following equation:

[tex]y(x) = {e^x} cos(x)[/tex]

and you want to know what the tangent (derivative) is at x=0? Do you know how to take the derivative of that y(x) function? Also, you won't be plugging in x=0 until you have that final derivative function...
 
I saw my mistake, I did the derivative wrong. sorry
 
cd246 said:
I saw my mistake, I did the derivative wrong. sorry

No need to be sorry. So that means you're okay now?
 
For this problem, Yes
 
Yeah, you forgot the chain rule.
 

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