The discussion centers on using implicit differentiation to find the derivative of the equation y = sin(x + y). The correct application of the chain rule leads to the derivative y' = cos(x + y) / (1 - cos(x + y)). The solution emphasizes the importance of proper parentheses in the final expression to avoid misinterpretation. Participants confirm the correctness of the approach and the necessity of clarity in mathematical notation.
PREREQUISITESStudents studying calculus, particularly those focusing on implicit differentiation, and educators looking for examples to illustrate the concept.
It's correct with the added parentheses.dylanhouse said:Homework Statement
I need to use implicit differentiation to find the derivative of y=sin(x+y).
Homework Equations
The Attempt at a Solution
This is what I did:
y=sin(x+y)
y'=(sin(x+y))'
y'=(1+y')(cos(x+y)) (by the chain rule)
Now, what do I do? Is this correct:
y'=cos(x+y)+cos(x+y)y'
y'-cos(x+y)y'=cos(x+y)
y'(1-cos(x+y))=cos(x+y)
y'= cos(x+y) / (1-cos(x+y) )
?