Задача 70981 Найти z''_(yy), если x+y+z = cos(x-z)...

643e8fb6dc8af77c5440385d

24.04.2023 12:27:28

Найти z''_(yy), если x+y+z = cos(x-z)

5f3ea7e3faf909182968ddd9

24.04.2023 12:47:39

★

(x+y+z)`_(y)=cos(x-z))`_(y)

0+1+z`_(y)=(-sin(x-z))*((x-z))`_(y)

1+z`_(y)=(-sin(x-z))*(0-z`_(y))

z`_(y)(sin(x-z)-1)=1

[m]z`_(y)=\frac{1}{sin(x-z)}


[m]z``_(yy)=-\frac{1}{sin^2(x-z)}\cdot (x-z)`_{y}[/m]

[m]z``_(yy)=-\frac{1}{sin^2(x-z)}\cdot (-z)`_{y}[/m]

[m]z``_(yy)=\frac{1}{sin^2(x-z)}\cdot z`_{y}[/m]

[m]z``_(yy)=\frac{1}{sin^2(x-z)}\cdot\frac{1}{sin(x-z)}[/m]

[m]z``_(yy)=\frac{1}{sin^3(x-z)}[/m]