Question

найти производную 2-го порядка $sqrt[5]{e^{7x-1}}$

Answer 1

$\y=sqrt[5]{e^{7x-1}}\ y'=(e^{7x-1})^{frac{1}{5}}\ y'=frac{1}{5}(e^{7x-1})^{-frac{4}{5}}cdot e^{7x-1}cdot7\ y'=frac{7}{5}(e^{7x-1})^{frac{1}{5}}\ y'=frac{7}{5}sqrt[5]{e^{7x-1}}$

 

$\y''=frac{7}{5}(frac{1}{5}(e^{7x-1})^{-frac{4}{5}}cdot e^{7x-1}cdot7)\ y''=frac{49}{25}(e^{7x-1})^{frac{1}{5}}\ y''=frac{49}{25}sqrt[5]{e^{7x-1}}$