Question

Найти dz/dx, если z= x-y/x+y

Answer 1

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Answer 2

To find dz/dx, we need to differentiate the expression z = (x - y)/(x + y) with respect to x. We will use the quotient rule of differentiation, which states that if we have a function u(x) = f(x)/g(x), then its derivative is given by:

du/dx = (f'(x) * g(x) - f(x) * g'(x)) / [g(x)]^2

Let's apply the quotient rule to find dz/dx for the given expression z = (x - y)/(x + y):

First, we need to find the derivatives of the numerator and denominator:

d(x - y)/dx = 1 - 0 = 1 d(x + y)/dx = 1 + 0 = 1

Now, using the quotient rule:

dz/dx = [(1 * (x + y) - (x - y) * 1) / (x + y)^2] = [(x + y - x + y) / (x + y)^2] = [2y / (x + y)^2]

So, the derivative dz/dx is:

dz/dx = 2y / (x + y)^2