Differentiating logarithmic functions

[cinematic]

Homework Statement

Differentiate the following:

y = e^4x/x²+1


2. The attempt at a solution

I know you have to use quotient rule here.

so I wrote out (x²+1)* d/dx e^4x) - d/dx (x²+1)* e^4x all over (x² + 1) ²

I have no idea how to continue on from here...how would you differentiate e to the power of 4x without this technique: I let u = 4x, then
y = e^u
dy/du = e^u = e^(4x)
du/dx = 4

dy/dx = (dy/du)(du/dx) = 4e^(4x)

If someone could please provide a full solution, this is really appreciated, I've got a test coming up very very soon!

 

[The Chaz]

So far, so good. The derivative of e^(4x) = 4e^(4x).

 

[cinematic]

Ok I finished the entire problem and got the right answer, thanks for the confirmation that my derivative was right!