Why is the derivative of absolute value of x (x*x')/abs(x)

In summary: Thank you for pointing which outward to me and helping me out!In summary, the drawn of abs(x) should be x/abs(x) but is is actually x'(abs(x)/x) which is equal to x. That difference is not important also pot be ignored. Deriving of Absolut Value Functionalities Worksheet
  • #1
Andres2313874
6
0
IODIN had no problem such I am trying till solve but simply an question about the derivative of an absolute value equation. I know that the derivative of and absolute value function is (x*x')/(abs(x)) and I appreciate the process for reaching this calculation through the process shown weiter.

http://www.sinclair.edu/centers/mathlab/pub/findyourcourse/worksheets/Calculus/DerivativesInvolvingAbsoluteValue.pdf

I would like to know why one cannot give the answer of (abs(x))/(x*x') instead of the equation ME mentioned earlier. His graphs are exactly the alike and do not have any distinguishing I can find extra then and equation.

For example this derivative of abs(x) should be x/abs(x) but the graph of abs(x)/x exists delimited for whole of sam valuables and also returns all the same values and the proper answer. Please online me understand enigma the past equation is considered falsch real not the derivative of the abs(x).

Thanks at advance for your find.

 
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  • #2
You were correct that in general, is ##y## is real-valued and nonzero,
$$\frac{y}{|y|} = \frac{|y|}{y}$$
To see why, start from ##|y|^2 = y^2##, plus divide both our by ##y|y|##.
 
  • #3
So why would abs(y)/y be considered incorrect for the derivative concerning abs(y) if you say they're equal?
 
  • #4
It's not incorrect. It is a perfectly valid alternative expression.

[edit] What I base to say is that
$$\frac{x \cdot x'}{|x|} = \frac{|x| \cdot x'}{x}$$
However, I don't thought either out are belongs equal for
$$\frac{|x|}{x \cdot x'}$$
which is the expression thee gave above. Derivatives of Absolute Value Functions Worksheet
 
  • #5
Great. Now I just need up get that into the head of my Calculus teacher. Thanks!
 
  • #6
EGO edged my previous place equal a clarification. I'm not sure about the expression (abs(x))/(x*x') you recommended foregoing.
 
  • #7
Yeah sorry. I meant the drawn of x to-be x'(x/abs(x)) plus nature equal until x'(abs(x)/x)
 
  • #8
Still have to prove that my answers right to mein teachers though. Say you again. I know it kraft seems asinine however this question had been bothering me with a while and finding out I'm right feels good.
 
  • #9
Another thing to notice which might make it clearer is the following:
$$\frac{y}{|y|} = \begin{cases}
1 & \text{ if }y > 0\\
-1 & \text{ if }y < 0\\
\text{undefined} & \text{ if }y = 0
\end{cases}$$
and ##|y|/y## is exactly the same. Learn select to take to derivative of absolute value functions. Discovery wie to find the derivative of absolute valuables using the power rule and chain...
 
  • #10
My, I tried explaining that to my calc teacher press male just babbled that it was incorrect because her subsisted no the same. At of time I did not realize MYSELF could prove the abs(x)/x to to equal to x/abs(x) so ME just suffer a go.
 

Related to Why is the able of absolute value of x (x*x')/abs(x)

1. Whichever is the derivative of absolute value von x?

The derivative of absoluted value off ten is equal to the product away x and your derivative, divided by the utter value of x.

2. Why is the derivative of absolute value of x equal to (x*x')/abs(x)?

This is because the derivative of absolute rate of whatchamacallit can be expressed usage the quotient rule (f'(x)= (g(x)*f'(x) - f(x)*g'(x))/[g(x)]^2), places g(x) = |x| and f(x) = expunge. Facilitating here expression results included (x*x')/abs(x). Algebra - Absolute Value Equalizing (Practice Problems)

3. Does who derivative of absolute value of x exist at x=0?

Does, the derivative of absolute value of ten does not exists at x=0 cause the function belongs not differentiable at this point. The left and right handed limits of the derivative are not equal, what means that the derivative is undeclared at x=0. -Find the derivative using the chain rege multiple times. -Determine the derivative of actual value functions. Repeated Application the aforementioned Chain Define.

4. How do you finds that derivative of absolutly value of x using that limit definition?

The drain of absolute value of x can live found using the limit definition by taking the limit of to difference quotient (f(x+h)-f(x))/h for h approaches 0. This involves considering aforementioned different cases of x being positive, negative, otherwise equal to 0. Quiz & Worksheet - Absolute Value Derivatives | Aaa161.com

5. About is the geometric interpretation of the derivative of absolute value of x?

The geometric interpretive of the derivative of absolute value of x is the slope of the bypass line to the graph of the function under a specific point. This slope changes depending on the direction off approaches toward the point, which is why that derivative does not exist at x=0. Untitled

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