Error propagation for non-linear regression parameters


I've been doing non-linear regression on some datasets using R. The regression outputs parameter estimation and parameter standard error (SE) for the three parameters a, n and k. I calculate the value for a new parameter f = n/k. I want to find the SE for f using error propagation. I found formulas at wikipedia for error propagation, but all are using standard deviation and not standard error. Can I use the same formulas for standard error?

SE formula:
f SE = SQRT((n/n SE)^2+(k/k SE)^2-2*covariance[n/k]/(n*k))*f

based on:
and :

Regression formula:
(c and day found in dataset)