2017年6月21日 · $\begingroup$ 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 derivative at that point does not exist. $\endgroup$ –

2018年4月10日 · What is the derivative of an absolute value? Calculus Basic Differentiation Rules Power Rule. 1 Answer

2021年4月27日 · 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 $\operatorname{sgn}$ is defined at that point, those two functions have distinct domains and therefore they cannot possibly be equal.

2015年8月14日 · Finding the derivative of an absolute value. Ask Question Asked 9 years, 6 months ago. Modified 5 years ago.

2021年7月24日 · 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 zero. So, the question is: Is the Sign Function a valid function to be the derivative of absolute value? Is there another function?

2015年4月15日 · Chain rule and the derivative of absolute value functions. 2. Finding derivative using product and chain ...

2018年10月8日 · The reason lies within “the limit definition of a derivative” I will jump to the explanation that sums it up since you have already stated f(x) at x=0 exists and there is continuity. The LIMIT of that “V” shape from the left MUST equal the …

2016年6月29日 · In addition, while a derivative is not necessarily a continuous function, it can be shown that any derivative must satisfy the "intermediate value property"- that is, given any two values of x, say x= a and x= b, somewhere between a and b, f must take on all values between f(a) and f(b). Of course, for x> 0, |x|= x so for x> 0, the derivative ...

2011年11月20日 · 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 get started.Please Help. Thank You

2021年8月29日 · Absolute Value derivative. 1. Solving a System of Equations with an Absolute Value. 0. Finding the ...