Using implicit differentiation, what is (dy)/(dx) if xy+4=x?

Rigoberto Drake

Rigoberto Drake

Answered question

2022-11-04

Using implicit differentiation, what is d y d x if x y + 4 = x?
I know the answer is 1 y x but I don't know how to get the answer.
So, I believe it is using a product rule. However, do I also need to use the chain rule?
What I did is
x y + 4 = x
I got x + y using the product rule so then,
x ( d y d x ) + y + 0 = 1
And is 4 a constant?
I am not sure the next step why d y d x belongs to x instead of y? Can anyone please explains this to me?

Answer & Explanation

cismadmec

cismadmec

Beginner2022-11-05Added 22 answers

x y + 4 = x
Differentiate both sides with respect to x; the product rule says d d x ( x y ) = d x d x y + x d y d x . So you get
y + x d y d x + 0 = 1 d y d x = 1 y x

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