You have the following function:
![y=3e^y+x](https://tex.z-dn.net/?f=y%3D3e%5Ey%2Bx)
Derivate implictly the previous expression, as follow:
![y^{\prime}=3e^yy^{\prime}+1](https://tex.z-dn.net/?f=y%5E%7B%5Cprime%7D%3D3e%5Eyy%5E%7B%5Cprime%7D%2B1)
Where you have used that:
![(e^y)^{\prime}=e^yy^{\prime}](https://tex.z-dn.net/?f=%28e%5Ey%29%5E%7B%5Cprime%7D%3De%5Eyy%5E%7B%5Cprime%7D)
Then, the implicit derivative of the given expression is:
![y^{\prime}=3e^yy^{\prime}+1](https://tex.z-dn.net/?f=y%5E%7B%5Cprime%7D%3D3e%5Eyy%5E%7B%5Cprime%7D%2B1)
Next, solve for y' as follow:
![\begin{gathered} y^{\prime}-3e^yy^{\prime}=1 \\ (1-3e^y)y^{\prime}=1 \\ y^{\prime}=\frac{1}{1-3e^y} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20y%5E%7B%5Cprime%7D-3e%5Eyy%5E%7B%5Cprime%7D%3D1%20%5C%5C%20%281-3e%5Ey%29y%5E%7B%5Cprime%7D%3D1%20%5C%5C%20y%5E%7B%5Cprime%7D%3D%5Cfrac%7B1%7D%7B1-3e%5Ey%7D%20%5Cend%7Bgathered%7D)
In 4 hours they will walk 14 miles
16:24 students made at least 80% on the test. The question is what is the ratio of students who scored below an 80% to the total number of students. 8:24 would be the right answer, but since it is asking for the answer in the simplest form, it would be 1:3.