Answer:
The ratio is 
Step-by-step explanation:
The question in English is
In a group of high school third graders, 38 are right-handed and 6 are left-handed. find the ratio of right-handed to left-handed
Let
x -----> number of students that are right-handed
y -----> number of students that are left-handed
we know that
To find out the ratio of right-handed to left-handed, divide the number of students that are right-handed by the number of students that are left-handed
so

we have

substitute

Simplify

Yes you used the chain rule properly to follow the correct steps to get the right answer. Great job.
If you wanted, you can come up with examples for f(x) and g(x) to help confirm the answer. A quick way to do this is to use something like GeoGebra to help graph the two expressions and you'll notice that the curves match up perfectly (indicating equivalent expressions). Note: GeoGebra can handle derivatives through the Derivative[] comand or you can type the function in the input bar with a tickmark after it to tell GeoGebra to derive the function.
To determine the ratio of the lengths of the red and blue ribbon, we just have to divide the lengths of the corresponding colored ribbon.
red / blue = 3/4 / 2/3 = 9/8
(2) The ratio of the lengths expressed as a unit rate is 9/8:1
(3) The ratio of the lengths of the blue to red ribbon is the reciprocal of the calculated value above giving us the answer of 8/9.
Turn 2/4 into 4/8
Because you cant halve the 5 in 5/8