Product Rule Clearification

[henlan]

Here is the picture of an example problem:


No matter how I look at it, I have no idea how the last line in the picture is found using the product rule on the expression found in part (a).

 

[Deleted member 4993]

Here is the picture of an example problem:
View attachment 7937

No matter how I look at it, I have no idea how the last line in the picture is found using the product rule on the expression found in part (a).

Instead of looking at it - did you work it out (step-by-step) with pencil and paper?

If you did, please share your work with us and we can correct it.

 

[henlan]

I'm just having some trouble understanding where exactly we apply the product rule. Is it between 2*r and dz/dx? As well as 2*s and dz/dy? Or is it between d/dr and the entire expression itself?

 

[stapel]

I'm just having some trouble understanding where exactly we apply the product rule. Is it between 2*r and dz/dx? As well as 2*s and dz/dy? Or is it between d/dr and the entire expression itself?

This works exactly the same way as when you were differentiating one-variable functions. If you'd been given "2x (dy/dx)" and been told to differentiate, what would you have done? Do the same thing here.