The discussion focuses on finding the derivative of the function y = e^(xy). The user attempts to apply logarithmic differentiation and the product rule but struggles to isolate the derivative. Key steps include using the equation y' [uv] = uv' + vu' and recognizing that y' can be expressed as y' = xy(y') + y^2. The solution involves rearranging the equation to factor out y' for further simplification.
PREREQUISITESStudents studying calculus, particularly those focusing on differentiation techniques, as well as educators looking for examples of implicit differentiation and logarithmic applications.
Looks like you're fine so far. Now move the xy(y') term to the left-hand side and factor out the y'. Can you go on from there?CeceBear said:Homework Statement
y= e^xy
y'= ?
Homework Equations
y' [a^x] = lna(a^x)
y' [uv] = uv' + vu'
The Attempt at a Solution
y = e^xy
lny = lne^xy
lny = xy(lne) = xy
(1/y)y' = (x)(y') + (y)(1)
y' = xy(y') + y^2
From here I don't know how to isolate the derivative. (And I feel like I shouldn't have done this implicitly...)