# How do you find the derivative of the function #f(x)=abs(x+1)#?

##### 1 Answer

Dec 27, 2016

# \ \ \ f'(x) = { (-1, x<-1), ("undefined", x=-1), (1, x> -1) :}#

#### Explanation:

The graph of

graph{|x+1| [-10, 10, -5, 5]}

# \ \ \\ \ \ f(x) = { (-(x+1), x+1<0), (0, x+1=0), (+(x+1), x+1> 0) :}#

#:. f(x) = { (-x-1, x<-1), (0, x=-1), (x+1, x> -1) :}#

And so:

# \ \ \ f'(x) = { (-1, x<-1), ("undefined", x=-1), (1, x> -1) :}#

If you use the formal definition of the derivative as a limit you can easily establish that at