Final answer:
To find the differential of z = e^{-9x} \cos(9t), we derive the partial derivatives with respect to x and t, giving us -9e^{-9x} \cos(9t)dx - 9e^{-9x} \sin(9t)dt.
Step-by-step explanation:
The student asked about finding the differential of the function z = e^{-9x} \cos(9t). To find the differential, we need to take the partial derivatives of z with respect to both variables x and t because z is a function of two variables. For the partial derivative with respect to x we get -9e^{-9x} \cos(9t), and for t, we get -9e^{-9x} \sin(9t). The total differential dz would then be -9e^{-9x} \cos(9t)dx - 9e^{-9x} \sin(9t)dt.