Проверить, удовлетворяет ли указанному уравнению с частными производными данная функция.

z=ln(x+e^(-y))

dz/dx=1/(x+e^(-y))*(x+e^(-y))'=1/(x+e^(-y))

d2z/dx2=((x+e^(-y))^(-1))'=-(x+e^(-y))^(-2)*(x+e^(-y))'=-1/(x+e^(-y))^2

d3z/dx2dy=(-(x+e^(-y))^(-2))'=-(-2(x+e^(-y)))^(-3)*(x+e^(-y))'=2(x+e^(-y))^(-3)*(-e^(-y))=-2e^(-y)/(x+e^(-y))^3

dz/dy=1/(x+e^(-y))*(x+e^(-y))'=1/(x+e^(-y))*(-e^(-y))=-e^(-y)/(x+e^(-y))

d2z/dydx=(-e^(-y)*(x+e^(-y))^(-1))'=-e^(-y)*((x+e^(-y))^(-1))'=

-e^(-y)*(-((x+e^(-y))^(-2)))*(x+e^(-y))'=e^(-y)/(x+e^(-y))^2

d3z/dydx2=(e^(-y)/(x+e^(-y))^2)'=e^(-y)((x+e^(-y))^(-2))'=

e^(-y)*(-2((x+e^(-y))^(-3)))*(x+e^(-y))'=-2e^(-y)/(x+e^(-y))^3

и все

-2e^(-y)/(x+e^(-y))^3-(-2e^(-y)/(x+e^(-y))^3)=-2e^(-y)/(x+e^(-y))^3+2e^(-y)/(x+e^(-y))^3=0

Объяснение:

y=-x^2+2x+3

xo=-b/2a

xo=-2/(-3)

xo=2/3

yo=-(2/3)^2+2(2/3)+3

yo=3 8/7

a)x^3-4x^2+16x+4x^2-16x+64=x^3+64

27a^3-45a^2+75a+45a^2-75a+125=27a^3+125