How do I Implicitly Differentiate this equation? My equation is y=x^(y^2)

Dillan Valenzuela

Dillan Valenzuela

Open question

2022-08-17

My equation is y = x y 2
I did the ln of both sides, then I tried implicit differentiation. I got
y = x y 2 y 2 x .

Answer & Explanation

ambivalentnoe1

ambivalentnoe1

Beginner2022-08-18Added 20 answers

y = x y 2
ln y = y 2 ln x
1 y d y d x = 2 y d y d x ln x + y 2 x
( 1 y 2 y ln x ) d y d x = y 2 x
( 1 2 y 2 ln x y ) d y d x = y 2 x
d y d x = y 3 x ( 1 2 y 2 ln x ) = y y 2 x ( 1 2 y y ln x )
d y d x = y 2 x y 2 1 1 2 y x y 2 ln x

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