The discussion revolves around using implicit differentiation to find dy/dx for the equation xey - 10x + 3y = 0. Participants are examining their approaches to differentiating the equation and comparing their results with a textbook answer.
Some participants have provided feedback on each other's differentiation processes, pointing out errors and suggesting corrections. There is an ongoing exploration of the differences in approaches to similar problems, with no explicit consensus reached on the correct method yet.
Participants mention the importance of clarity in notation and the potential for confusion when notating equations. There is also a reference to a textbook answer that differs from some participants' calculations, indicating a need for careful consideration of parentheses and terms in the differentiation process.
The first thing wrong is starting the line below with =. By putting that = at the start of each line, you are more likely to lose track of the two sides of the equation you started with.domyy said:Homework Statement
Use implicit differentiation to find dy/dx.
Homework Equations
xey - 10x + 3y = 0
The Attempt at a Solution
The more serious mistake is above. You didn't take the derivative of xey correctly. d/dx(xey) = ey + xey*y'. Do you see why?domyy said:= [xey + ey(y)'] - (10x)' + (3y)' = 0
No, I believe their answer is (10 - ey)/(xey + 3). Note the parentheses, and the 3 instead of the 3y that you had.domyy said:= xey + ey(y') - 10 + 3(y') = 0
= y' (ey + 3) = 10 - xey
= y' = 10 - xey/ ey + 3y
However, my book says the answer: 10 - ey/ xey + 3y.
domyy said:What am I doing wrong?
Thanks!
Don't start your work with =.domyy said:About taking the derivative wrongly, my question is: How does that differ from y= xe^x - e^x?
Because I was trying to follow the same thinking when solving the problem in question.
This is how I solved it ( and I got it right):
In this problem,domyy said:= xe^x + e^x (x)' - e^x(x)'
= xe^x + e^x - e^x
= e^x ( x -1 + 1)
= xe^x
Thanks!