Jun 21, 2017 · The absolute value function has a derivative (s) on restricted domains. i.e. f' (x) = -1 for x <0 and f' (x) = 1 for x > 0. However, the absolute value function is not "smooth" at x = 0 so the …

Apr 27, 2021 · And, when that happens, the derivative is indeed $\operatorname {sgn} (x)$ or $\frac x {|x|}$. But, since the derivative of the absolute value function is undefined at $0$, but $\operatorname …

Apr 15, 2015 · Find the derivative of absolute value using the chain rule Ask Question Asked 10 years, 8 months ago Modified 5 years, 8 months ago

Jul 24, 2021 · 4 If you differentiate the absolute value function the result could be the Sign Function. By definition, the Sign Function is defined at 0, but there is no derivate of absolute value function at …

Aug 14, 2015 · To elaborate on Dr. MV's answer, we can find the derivative of the absolute value function by noting $$ |x|=\sqrt {x^2}$$ and then using the chain rule. The proof goes:

Nov 20, 2011 · Please Help me derive the derivative of the absolute value of x using the following limit definition. $$\lim_ {\Delta x\rightarrow 0}\frac {f (x+\Delta x)-f (x)} {\Delta x} $$ I have no idea as to …

How to handle derivative of absolute value? Ask Question Asked 10 years, 9 months ago Modified 10 years, 9 months ago

Apr 3, 2023 · In high school calculus, I am in the unit on antidifferentiation and its applications. One of its applications is finding distances with a velocity function. You can use this to find both net dista...

At the origin, the absolute value function "bends" - it goes from decreasing with a slope of -1 to increasing with a slope of 1.

Aug 29, 2021 · If $x\le0$, then $f (x)=-x^3$ has derivative $-3x^2$; so the left derivative at $x=0$ is $0$. So the left derivative is equal to the right derivative, and therefore the derivative is their common …