Question

e la -x derivat de doua ori

Answer 1

e la -x ii e la x ori (-1).
derivat inca o data ii e la -x.

Answer 2

$(e^{-x})^{''} = \Big((e^{-x})'\Big)' = \Big(e^{-x}\cdot (-x)'\Big)' = \Big(e^{-x}\cdot (-1)\Big)' =(-e^{-x})' = \\ \\ =-(e^{-x})' = -\Big(e^{-x}\cdot (-x)'\Big) = -\Big(e^{-x}\cdot (-1)\Big) = -(-e^{-x}) = e^{-x} \\ \\ \\ M-am folosit de: \left\| \begin{array}{c} Proprietatea: (a\cdot u)' = a\cdot (u)', (a - constanta ) \\ Formula: (e^{u})' = e^u\cdot u'\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \end{array} \right|$

$\\ Poti calcula si mai la indemana asa: \\ \\ (e^{-x})'' = ? \\ \\ (e^{-x})' = e^{-x}\cdot (-x)' = e^{-x}\cdot (-1) = -e^{-x} \\ \\ \Rightarrow (e^{-x})'' = (-e^{-x}) ' = -\Big(e^{-x}\cdot (-x)'\Big) = -\Big(e^{-x}\cdot (-1)\Big) = e^{-x}$