Mastering Tricky Derivative Problems: Solving for dy/dx with x^2*y-e^2x=sin(y)"

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Homework Help Overview

The problem involves finding the derivative dy/dx for the equation x^2*y - e^(2x) = sin(y), which suggests a context of implicit differentiation and calculus.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the challenges of solving for y explicitly and explore the concept of implicit differentiation. Questions arise about differentiating sin(y) with respect to x and the application of the chain rule.

Discussion Status

The discussion is active, with participants offering reminders about implicit differentiation and exploring how to apply the chain rule to the differentiation of sin(y). There is no explicit consensus on the approach yet.

Contextual Notes

Participants are navigating the complexities of implicit differentiation and the specific roles of y as a function of x within the equation.

blue mango
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Homework Statement



if x^2*y-e^2x=sin(y) find dy/dx


The Attempt at a Solution



I tried solving for y but that seems quite impossible so I was wondering if anyone had any other suggestions on possible solutions. Thanks
 
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Do you know what implicit differentiation is?
 
yes...thanks for reminding me of that. the left side isn't a problem but how do you differentiate sin(y) with respect to x?
 
actually wouldn't it just be 0? then dy/dx is e^2x/x
 
You have sin(y). y is a function of x so you could write this as sin(y(x)). Then use the chain rule
 

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