Question

Найти производную d^2z/dxdy функции z=ln(x^2+e^-2y)

Answer 1

$y=ln(x^2+e^{-2y})\\frac{partial z}{partial x}= frac{1}{x^2+e^{-2y}} cdot 2x= frac{2x}{x^2+e^{-2y}} \\ frac{partial ^2z}{partial xpartial y} = frac{-2x(-2e^{-2y})}{(x^2+e^{-2y})^2} = frac{4xe^{-2y}}{(x^2+e^{-2y})^2}$