What is 2xy differentiated implicitly?

Ian Lindsey

Ian Lindsey

Answered question

2023-03-23

What is 2xy differentiated implicitly?

Answer & Explanation

Santino Potter

Santino Potter

Beginner2023-03-24Added 8 answers

I'll assume that since the question doesn't say with respect to what, y is a function of x.
Use the product rule:
y = d ( u . v ) d x = v . d u d x + u . d v d x
So:
y = 2 x . y + y 2 . d x d x
y = 2 x . y + 2 y
y = 2 y 1 - 2 x
punctator2ueu

punctator2ueu

Beginner2023-03-25Added 8 answers

The function is
f ( x , y ) = 2 x y
Partially derivatives include
f x = 2 y
f y = 2 x
Hence,
d y d x = - f x f y = - 2 y 2 x = - y x

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