Question

Use implicit differentiation for the function: yz = ln(x+z) to find the partial derivative of both y and z in respect to x

Answer 1

Any ideas on how to start this question?

Answer 2

for \(\dfrac{\partial z}{\partial x}\) just do normal implicit diff with \(z = z(x)\) and \(y = const\)

vice versa for \(\dfrac{\partial y}{\partial x}\)

that make sense?!

Answer 3

yeah I got something like:
\[ \frac{ ∂y}{ ∂x }z = \frac{ 1 }{ x+z }\]

Answer 4

Does it seem about right?
And then from here, I would make ∂y/∂x the subject

Answer 5

looks good

Answer 6

yeah. make it the subject

Answer 7

Okay cool, I guess this would also be a similar outcome for ∂z/∂x

Answer 8

for z, i get

\( y \dfrac{\partial z}{\partial x} = \dfrac{1}{x+z} (1 + \dfrac{\partial z}{\partial x})\)

and then tidy up

Answer 9

Okay cool got it!