Final answer:
To find the differential of the function y = tan(√3t), apply the chain rule. The differential is dy = sec²(√3t) * √3 dt.
Step-by-step explanation:
To find the differential of the function y = tan(√3t), we need to apply the chain rule. The chain rule states that if u = f(g(t)), then du/dt = f'(g(t)) * g'(t). In this case, f(u) = tan(u) and g(t) = √3t. So, differentiating f(u) with respect to u gives us f'(u) = sec²(u), and differentiating g(t) with respect to t gives us g'(t) = √3. Therefore, the differential of y = tan(√3t) is dy = sec²(√3t) * √3 dt.