simple q, partial derivative writing formally with function having both implicit and explicit dependence on variable

Question

I have the function $L$ which depends on other variables as well as $n$ explicitly and implicitly as below.

$$\frac{\partial L}{\partial n} = \frac{\partial L}{\partial e}\frac{\partial e}{\partial n} + \frac{\partial L}{\partial p}\frac{\partial p}{\partial n} + \frac{\partial L}{\partial n}$$

This looks wrong ofc, I feel like the LHS should be written as the total derivative to make it look right, however, it is the partial derivaitve I am taking right? so?

Thanks in advance.

Answer 1

I think you need to take away the partial L with respect to n on the right-hand side and then it should be correct. (Sorry about not writing proper notation I'm new on this site).