Find the differential of the function: `u=e^{-sin(s+2t)}` 

Expert Answers
lfryerda eNotes educator| Certified Educator

In order to find the differential of a function, we need to take the partial derivatives of the function with respect to each of the variables, and then combine them according to the formula (see link below):

`du={partial u}/{partial s} ds+{partial u}/{partial t} dt`

In each case, we take the partial derivative assuming the other variable is constant, so:

`{partial u}/{partial s}=e^{-sin(s+2t)}(-cos(s+2t))`



`{partial u}/{partial t}=e^{-sin(s+2t)}(-cos(s+2t))(2)`


which means that the differential becomes:


The differential of the function is `du=-cos(s+2t)e^{-sin(s+2t)}ds-2cos(s+2t)e^{-sin(s+2t)}dt` .