Question

Найти первую вторую производную

Answer 1

$LARGE \ left{begin{matrix} x=e^{-2t} \ y=e^{t} end{matrix}right.; ; ; left{begin{matrix} x'_t=-2e^{-2t}\ y'_t=e^t end{matrix}right.\ boldsymbol{y'_x={y'_tover x'_t}=-{e^tover2e^{-2t}}=-{e^{3t}over2}}\ (y'_x)'_t=-{3e^{3t}over2}\ boldsymbol{y''_x={(y'_x)'_tover x_t}={3e^{3t}over4e^{-2t}}={3e^{5t}over4}}$