The discussion focuses on finding the derivative dy/dx for the equation Y^x = X^y using logarithmic differentiation. Participants emphasize the importance of differentiating equivalent forms of the equation, specifically using natural logarithms to simplify the process. The correct differentiation technique involves applying the properties of logarithms, such as Ln(Y^x) = Ln(X^y), leading to the equation X • Ln(y) = Y • Ln(x). Participants clarify the distinction between "differentiate" and "derive," asserting that improper terminology can lead to confusion.
PREREQUISITESStudents studying calculus, particularly those tackling implicit differentiation and logarithmic functions, as well as educators seeking to clarify terminology and techniques in derivative calculations.
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.