Arctan(y)=3x+y how would I go about finding y'?

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Homework Help Overview

The discussion revolves around the implicit differentiation of the equation arctan(y) = 3x + y, with a focus on finding the derivative y'. Participants are exploring the application of differentiation techniques in this context.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Some participants attempt to manipulate the original equation to isolate y, while others question the validity of these steps. There is a discussion on using implicit differentiation and the chain rule, with specific inquiries about the differentiation of arctan(y) and the correct application of derivatives.

Discussion Status

The conversation is ongoing, with various interpretations of the differentiation process being explored. Some participants have offered guidance on using implicit differentiation, while others are clarifying the steps involved in differentiating arctan(y). There is no explicit consensus on the correct approach yet.

Contextual Notes

Participants are grappling with the implications of the original equation and the appropriate methods for differentiation, indicating a need for clarity on implicit differentiation rules. There is also mention of potential confusion regarding the notation used in derivatives.

IllmicIll
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Homework Statement



Arctan(y)=3x+y how would I go about finding y'?

Homework Equations





The Attempt at a Solution



I tried to start out with...

arctan(y)= tan(x)
tan(x)=3x+y
tan(x)-3x=y

y'=1/(1+x^2) -3

is this correct?
thanks in advance.
 
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IllmicIll said:
arctan(y)= tan(x)

How you reached here from
Arctan(y)=3x+y ?

What's
d/dx (Arctan(y)) ?
Use the chain rule.
 


How can arctan(y)=tan(x) when your equation says arctan(y)=3x+y?? That's not right. Don't try to solve for y. You can't. Differentiate it implicitly.
 


d/dx arctan y

y'/1+y^2*y' ?
 


IllmicIll said:
d/dx arctan y

y'/1+y^2*y' ?

Close. But why are there two y' in there? And use parentheses to avoid confusion. There's a difference between 1/1+y^2 and 1/(1+y^2).
 


y'/(1+y^2) *y'
I thought the 2nd y' has to be there bc for example
y=arccot(x^2)
x^2=cot y
2x=-csc^2(y) *y'

is that not the case since I already have a y'?
 


oops nvm...
 

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