When should I use total differentials and when should I use implicit differentiation? An example of an equation where I'm unsure if to use total differentials or implicit differentiation is f(x,y)=x^2y

kadejoset

kadejoset

Answered question

2022-07-16

When should I use total differentials and when should I use implicit differentiation?
An example of an equation where I'm unsure if to use total differentials or implicit differentiation is f ( x , y ) = x 2 y
Using total differentials
f x d x + f x d y = 2 x y d x + x 2 d y, solving for d y d x = 2 y x
Using implicit differentiation:
( 2 x d y d x ) ( y ) + x 2 , solving for d y d x = x y
I'm unsure when to use each method and they both yield different results.

Answer & Explanation

Mireya Hoffman

Mireya Hoffman

Beginner2022-07-17Added 14 answers

If f x j = f x j then
d f = f x d x + f y d y = 2 x y d x + x 2 d y

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