# Implicit Differentiation z=f(x/y) meaning

1. Jan 2, 2016

### xoxomae

Mod note: Moved from the Homework section
1. The problem statement, all variables and given/known data

This might seem like a stupid question but I'm unsure what z= ƒ(x/y) means? I'm not sure how I would find ∂z/∂x , ∂z/∂y just from this statement either.

Thank you
2. Relevant equations

3. The attempt at a solution

Last edited by a moderator: Jan 2, 2016
2. Jan 2, 2016

### PeroK

You could try taking $f$ to be some simple function. For example $f(X) = X^2$, where I've used $X$ to define the function to avoid confusion with $x, y$.

3. Jan 2, 2016

### Staff: Mentor

It means that z is a function of the quotient x/y. For example, $z = (x/y)^2 + 3(x/y)$

To find the partial derivatives, you'll need to use the chain rule.

4. Jan 2, 2016

### xoxomae

I'm sorry, I'm just really unsure how to apply the chain rule. So is ∂z/∂t = ∂/∂x(x/y) * F' ? But I'm unsure how to find all the other ones. I have the solutions attached to this post but I have no idea how to get them.
Thank You

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5. Jan 2, 2016

### vela

Staff Emeritus
What are $t$ and $F$?

Can you calculate $\frac{\partial z}{\partial x}$ if $z=f(u(x,y))$ where $u$ is a function of $x$ and $y$?

6. Jan 2, 2016

### xoxomae

So i would let u=x/y so then

$$\frac{\partial z}{\partial x} = \frac{\partial z }{\partial u} \frac{\partial u }{\partial x} = \frac{f'}{y}$$

cause I'm guessing $$\frac{\partial z }{\partial u} = f'$$ or am i completely wrong?

7. Jan 2, 2016

### vela

Staff Emeritus
That's right.