Question

U(x,y)=x^2-y^2, Найти: 1) w'=(U+iV)' 2) U

Answer 1

Ответ:

Y=(3x)^-1/2+(3x)^1/2 найти y'(1/3)

Пошаговое объяснение:

Y=(3x)^-1/2+(3x)^1/2 найти y'(1/3)

Answer 2

To find the derivative of a complex function, we can treat the real and imaginary parts separately. Let's start by finding the real part of the derivative w' = (U + iV)':

1. Finding the real part of w':

Let's express U in terms of x and y: U(x, y) = x^2 - y^2

To find the derivative of U with respect to x, we treat y as a constant: ∂U/∂x = 2x

To find the derivative of U with respect to y, we treat x as a constant: ∂U/∂y = -2y

The real part of w' is obtained by taking the derivative of U with respect to x and subtracting the derivative of U with respect to y:

Re(w') = ∂U/∂x - ∂U/∂y = 2x - (-2y) = 2x + 2y

2. Finding U:

We already have U(x, y) = x^2 - y^2 as given.

Therefore, U = x^2 - y^2.

So, the real part of the derivative w' is 2x + 2y, and U(x, y) = x^2 - y^2.