Final answer:
The differential of the function y=tan(x) is dy = sec^2(x) dx, which is obtained by taking the derivative of tan(x) with respect to x.
Step-by-step explanation:
The student has asked for the differentiation of the function y=tan(x). To find the differential dy, we use the derivative of the tangent function with respect to x. The derivative of y=tan(x) is found using the formula:
dy/dx = sec^2(x).
Thus, the differential dy equals sec^2(x) dx. This is because the derivative of tan(x) with respect to x is sec^2(x), and the differential dy is the product of this derivative and the infinitesimal change in x, denoted dx.