Question

Найти первую вторую производную

Answer 1

$\LARGE \\ \left\{\begin{matrix} x=e^{-2t} \\ y=e^{t} \end{matrix}\right.\; \; \; \left\{\begin{matrix} x'_t=-2e^{-2t}\\ y'_t=e^t \end{matrix}\right.\\ \boldsymbol{y'_x={y'_t\over x'_t}=-{e^t\over2e^{-2t}}=-{e^{3t}\over2}}\\ (y'_x)'_t=-{3e^{3t}\over2}\\ \boldsymbol{y''_x={(y'_x)'_t\over x_t}={3e^{3t}\over4e^{-2t}}={3e^{5t}\over4}}$