Final answer:
To find the differential dy for y = e^{x/5}, differentiate y with respect to x to get dy/dx = (1/5)e^{x/5}, thus dy = (1/5)e^{x/5}dx.
Step-by-step explanation:
The student is asking about finding the differential dy for the function y = e^{x/5}. To find dy, we need to take the derivative of y with respect to x, which gives us dy/dx. Using the chain rule, dy/dx = (1/5)e^{x/5}. Hence, the differential dy is (1/5)e^{x/5}dx. This step-by-step process aligns with the concepts of calculus and differentiation, specifically dealing with exponential functions.