Implicit Differentiation Quesrion x^y=y^x is the equation My solution is : dy.dx=(lny−y/x)/(lnx−x/y)

Eisregiony1

Eisregiony1

Open question

2022-08-29

x y = y x
is the equation
My solution is :
d y d x = ( ln y y x ) / ( ln x x y )
Just wondering if this is correct!

Answer & Explanation

Tess Pollard

Tess Pollard

Beginner2022-08-30Added 8 answers

Both are correct. Notice that
( ln y y x ) ( ln x x y ) = x ln y y x y y ln x x
By the nature of the function we have x ln y = y ln x, therefore
d y d x = y ln x y x y x ln x x = ln x 1 x 2 y 2 ln y 1

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