Question

Find the derivative of 3e^y+x=y

Answer 1

You have the following function:

`y=3e^y+x`

Derivate implictly the previous expression, as follow:

`y^(\prime)=3e^yy^(\prime)+1`

Where you have used that:

`(e^y)^(\prime)=e^yy^(\prime)`

Then, the implicit derivative of the given expression is:

`y^(\prime)=3e^yy^(\prime)+1`

Next, solve for y' as follow:

`\begin{gathered} y^(\prime)-3e^yy^(\prime)=1 \\ (1-3e^y)y^(\prime)=1 \\ y^(\prime)=(1)/(1-3e^y) \end{gathered}`