唔識做啊><要有步驟.thankyou

Your question just ask you to "find", not "find directly from the first principle".

According to the differentiation rule derived from the first principle, we have dtc/dt = ct(c - 1), so we have

s = 4 + t-1/2
s' = (-1/2) * t-3/2

Okay, I don't fool you...

s' = lim_{q -> 0}{ [4 + (t + q)-1/2 - (4 + t-1/2)] / q}
= lim_{q -> 0}{[(t + q)-1/2 - t-1/2] / q}
= lim_{q -> 0}{[(t + q)-1/2 - t-1/2][(t + q)-1/2 + t-1/2)] / q[(t + q)-1/2 + t-1/2]}
= lim_{q -> 0}{[1/(t + q) - 1/t] / q[(t + q)-1/2 + t-1/2)]}
= lim_{q -> 0}{[t - (t+q)] / t(t + q)q[(t + q)-1/2 + t-1/2)]}
= lim_{q -> 0}{-q / t(t + q)q[(t + q)-1/2 + t-1/2]}
= lim_{q -> 0}{-1 / t(t + q)[(t + q)-1/2 + t-1/2]}
= lim_{q -> 0}{-1 / [t(t + q)1/2 + t1/2(t + q)]}
= 1 / [t(t)1/2 + t1/2(t)]
= -(1/2) * t-3/2