The Mystery of Green-Colored Steps: A Homework Tutorial

[athrun200]

Homework Statement

Homework Equations

The Attempt at a Solution

In part a, there is an important step, I don't know how to have the step that written in green colour.
Does this technque have any name?
Can you give me more example of it?

 

[bp_psy]

You just manipulate the differentials.
$\frac{d \dot{r}}{dt}=\frac{d \dot{r}}{dt} \frac{dr}{dr}=\frac{d \dot{r}}{dr} \frac{dr}{dt}=\dot{r} \frac{d \dot{r}}{dt}$

edit. corrected last part

 

[athrun200]

You just manipulate the differentials.
$\frac{d \dot{r}}{dt}=\frac{d \dot{r}}{dt} \frac{dr}{dr}=\frac{d \dot{r}}{dr} \frac{dr}{dt}=\dot{r} \frac{dr}{dr}$

It is quick difficult to think of this step.
If I don't check the solution, I wouldn't write out this.

 

[bp_psy]

It is quick difficult to think of this step.
If I don't check the solution, I wouldn't write out this.

It appears that I messed up the last equality. I corrected the last post.
It is clearer if you see that it is the chain rule.
let $\dot{r}=\dot{r}(r(t))$ then $\frac{d \dot{r} }{dt}=\frac{d \dot{r} }{dr} \frac{d{r} }{dt}$