Question

Simplify the function f(t) = sinh(ln(t)). Then, find the derivative of your simplified form of f(t).

Answer 1

We first consult the hyperbolic definition of sinh t. The expression is equal to (e^t - e^-t) / 2. since there is ln t inside, the appropriate equivalent should be (e^ln t- e^- ln t) / 2. This is equal to (t + t) /2 equal to t. The differential is equal to 1.