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 . . .