Question 410752
First of all, according to what you have written, f(x) is a function in terms of t, not x, implying that f(x) is some constant and the derivative is 0 (If it was a function in terms of x and t it would be denoted f(x,t)). However we can let


{{{f(t) = t^(2/3) + 2(t^(3/2))}}}. Applying the power rule,


{{{(d/dt)(f(t)) = (2/3)t^(-1/3) + 2*(3/2)t^(1/2) = (2/3)t^(-1/3) + 3t^(1/2)}}}