Question

Найдите производную функции s=t/e^t и вычислите s`(0)

Answer 1

$s= \frac{t}{e^{t}}\\\\s'= \frac{e^{t}-t\cdot e^{t}}{e^{2t}}=\frac{e^{t}\cdot (1-t)}{e^{2t}}= \frac{1-t}{e^{t}}\\\\s'(0)= \frac{1-0}{e^0}= \frac{1}{1}=1$