Question

Найти производную функции |x|+1 и область определения

Answer 1

Производная 
$y=(|x|+1)'=sign(x)\\D(y)=R$
sign(x) это производная функции модуля

Answer 2

Derivative of the Absolute Value Function and Its Domain

The derivative of the absolute value function |x| can be found by using the definition of the absolute value function and applying the rules of differentiation. The absolute value function |x| can be defined as:

|x| = x, if x ≥ 0 |x| = -x, if x < 0

To find the derivative of |x|, we can use the piecewise definition and apply the rules of differentiation to each piece.

For x ≥ 0: The derivative of x is 1, so the derivative of |x| for x ≥ 0 is 1.

For x < 0: The derivative of -x is -1, so the derivative of |x| for x < 0 is -1.

Therefore, the derivative of the absolute value function |x| is: f'(x) = 1, if x > 0 f'(x) = -1, if x < 0

The domain of the absolute value function |x| is all real numbers, denoted as R.

Cited Sources

1. Source Title: ' , . ' 2. Source Title: ': '

I hope this helps! If you have further questions or need additional assistance, feel free to ask.