If y = x/z then how do you calculate dx/dy?

[confused88]

sorry I am so dumb, coz i forgot all maths over the holidays..

but if y = x/z
then how do you calculate dx/dy?

 

[jgens]

Well, if $y = x/z$ then $z*y = x$. Does that help? If $z$ is a variable and not a constant, then you'll need to use partial derivatives.

 

[confused88]

haha i think that you underestimate how dumb i am. But that's cool, thanks for the help but

 

[jgens]

Well, if $z$ is a constant, then this derivative is a simple application of the power rule:

$$\frac{d}{dy}(zy) = z = \frac{dx}{dy}$$

If $z$ is not a constant but a function rather, then we use partial derivatives so that we have:

$$\frac{\partial}{\partial y}(zy) = z = \frac{\partial x}{\partial y}$$

It's also easy to derive these results using the definition of a derivative . . .