Final answer:
To find the differential of y = etan(t), we can use the chain rule. The derivative of y with respect to t is given by dy/dt = e^tan(t) * sec^2(t). The correct option is a) esec²(t).
Step-by-step explanation:
To find the differential of y = etan(t), we can use the chain rule.
To do this, we need to use the chain rule for differentiation, which requires us to multiply the derivative of the outer function by the derivative of the inner function.
The chain rule states that if we have a function f(g(x)), then the derivative is given by f'(g(x)) * g'(x).
In our case, f(g(x)) = e^x and g(x) = tan(x). So, the derivative of y with respect to t is given by:
dy/dt = e^tan(t) * sec^2(t)
Therefore, the correct option is a) esec²(t).