# Derivative of (2/x) + (1/y) = 4 and

1. Aug 15, 2012

### autodidude

Can you somehow show that the derivative of $$\frac{2}{x}+\frac{1}{y}=4$$ is the same as $$2y+x=4xy$$ if x≠0 and y≠0? Or is that not true?

2. Aug 15, 2012

### chiro

Yes you can do this (provided your condition that you have non-zero values for y and x) since algebraically both are equivalent (again assuming non-zero values).

The rest is going to be implicit differentiation, but again you have to consider that there will be holes at x = 0 and also at y = 0 where the function is defined for either of these values.

3. Aug 15, 2012

### autodidude

Thanks chiro. To do so, would you just differentiate each equation and manipulate one of the derivatives until it's equivalent to the other? (again, with x and y no equal to 0

4. Aug 15, 2012

### Dickfore

You don't even have to do that much. just multiply the original equation by $x y$. You will get the second equation. Multiplying by $x y$ is justified only when:
$$x y \neq 0 \Leftrightarrow x \neq 0 \wedge y \neq 0$$

5. Aug 15, 2012