# Thread: Derivative of function f(x)=x|x|

1. ## Solved

For the function f(x)=x|x|, show that f'(0) exists. wht is the value?

2. $f(x)= |x| = x, x\geq 0 \implies f'(x)=1$

$f(x)= |x| = -x, x< 0 \implies f'(x)=-1$

Maybe use the product rule from here?

3. $|x|$ is not differentiable at $x = 0$, so what makes you think that $x|x|$ is differentiable there?

4. x|x| = sgn(x) * x^2

5. $f'(0)= \lim_{h\to 0}\frac{f(h)- f(0)}{h}$

For f(x)= x|x|, this is $f'(0)= \lim_{h\to 0}\frac{h|h|- 0}{h}= \lim_{h\to 0}|h|= 0$.

Yes, Prove It, even though |x| is not differentiable at x= 0, x|x| is!

6. Posted by pickslides from this thread:
http://www.mathhelpforum.com/math-he...on-153220.html
Wow this is really similar to http://www.mathhelpforum.com/math-he...on-153221.html

Are you in the same class or the same person?
Interesting... Here is another instance of alexprem and ilovemymath posting the exact same question.

http://www.mathhelpforum.com/math-he...ve-153114.html

Coincidence?

7. might be someone from my class
because we are taking this over online so many of us will have problem as we are not being taught anything

8. Originally Posted by ilovemymath
might be someone from my class
because we are taking this over online so many of us will have problem as we are not being taught anything
... such is the major pitfall of "online" classes ... we see many who come here with little or no background in the subject matter for the course they are attempting. I seriously question their academic value.