The discussion revolves around finding the derivative dy/dx for the equation Y^x = X^y, which involves logarithmic differentiation and the application of implicit differentiation techniques.
The conversation includes attempts to clarify terminology, such as the distinction between "differentiate" and "derive." There is an ongoing exploration of the implications of different approaches to differentiation without reaching a consensus on the best method.
Participants note that there may be concerns about the safety of certain methods as indicated by an instructor, suggesting that some approaches could lead to incorrect solutions.
To find a derivative, you differentiate. The word derive means something else.Mamdoh Abughalion said:Homework Statement
.[/B]
Find dy/dx
Y^x = X^y
Homework Equations
F'( Ln(x)) = 1/x
Lnx^y = yLnx
The Attempt at a Solution
Ln(Y^x) = Ln(X^y)
X • Lny = Y • Lnx , should I derive now or :
Y = X • Lny/Lnx
Y = X • Logxy , then derive?
I know that , but my instructer told me that the second way is too much " dangerous " and may lead to wrong solution .Orodruin said:It does not matter when you differentiate as long as the equality you are differentiating is equivalent to the original one.