Understanding the Product Rule for Differential Operators

[zezima1]

From my book:

Let

h = x + ay and g = x + by

By product rule we then have:

∂/∂x = ∂/∂h + ∂/∂g

Can someone explain to me how to arrive at this result? I don't even get what ∂/∂x even means, isn't it just a differential operator?

 

[SammyS]

From my book:

Let

h = x + ay and g = x + by

By product rule we then have:

∂/∂x = ∂/∂h + ∂/∂g

Can someone explain to me how to arrive at this result? I don't even get what ∂/∂x even means, isn't it just a differential operator?

Yes, ∂/∂x is an operator.

Do you know the definition of $\displaystyle \frac{\partial F(x,\,y)}{\partial x}$, and/or how to evaluate this partial derivative given the function, F(x, y) ?

 

[zezima1]

yes yes I know all that, I just can't specifically see how they arrive at the result using the product rule :)

 

[SammyS]

yes yes I know all that, I just can't specifically see how they arrive at the result using the product rule :)

Off hand, I don't see the result as coming from the product rule either.