If z is defined implicitly as a function of x and y, find ∂ z...

Uroskopieulm

Uroskopieulm

Answered

2022-11-22

If z is defined implicitly as a function of x and y, find z x
  y z = l n ( x + z )
I've attempted this equation going forward with implicit differentiation and I've used the theorem that states z x = F / x F / z

Answer & Explanation

Ryan Davies

Ryan Davies

Expert

2022-11-23Added 18 answers

Given:
  y z = ln ( x + z ) y z ln ( x + z ) = 0 F ( x , y , z ) = 0 ,
we find:
z x = z x = F / x F / z = F x F z = 1 x + z y 1 x + z = 1 x y + y z 1 ..
Noe Cowan

Noe Cowan

Expert

2022-11-24Added 4 answers

This should be:

Partially differentiating both sides with respect to x:
y   z x = 1 x + z ( 1 + z x )
Now you can rearrange and obtain the correct value.

This way works because z is an implicit function of x and y.

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