Question

X=y + arctg y производная

Answer 1

Ответ:

$x'=1+\frac{1}{1+y^2}$

Пошаговое объяснение:

Answer 2

To find the derivative of the expression X = y + arctan(y), we can use the rules of differentiation. Let's differentiate each term separately:

1. Differentiating y with respect to y gives us 1.
2. Differentiating arctan(y) with respect to y requires the chain rule. The derivative of arctan(u) with respect to u is 1 / (1 + u^2). So, applying the chain rule, we have d(arctan(y))/dy = (1 / (1 + y^2)) * dy/dy = 1 / (1 + y^2).

Now, we can add the derivatives together:

dX/dy = 1 + 1 / (1 + y^2)

Therefore, the derivative of X with respect to y is 1 + 1 / (1 + y^2).