Derivative of -x using first principle

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Homework Help Overview

The discussion revolves around finding the derivative of the function -x using the first principle of derivatives. Participants are exploring the application of the definition of the derivative and questioning the setup of the function evaluations.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to apply the first principle by substituting into the derivative formula but questions the outcome of their calculations. Other participants clarify the function evaluations and express confusion about the correct form of f(x+h).

Discussion Status

Participants are actively engaging with the problem, with some providing insights and corrections regarding the function evaluations. There is a productive exchange of ideas, though no consensus has been reached on the original poster's calculations.

Contextual Notes

There appears to be confusion regarding the correct evaluation of f(x+h) for the function -x, which is central to the discussion. The original poster's approach and the responses highlight the importance of accurately applying the first principle of derivatives.

rishi kesh
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Homework Statement


This is a silly question,but i have a problem.How do we solve derivative of -x using first principle of derivative. I know that if derivative of x w.r.t x is 1 then ofcourse that of -x should be -1. Also it can be solved by product rule taking derivative of -1.x .

Homework Equations

The Attempt at a Solution


Here is how i attempted it:
f(x)= -x
f(x+h)= -x+h
Using first principle :
dy/dx = [-x+h-(-x)]/h
= h/h
= 1
what is wrong here?please help. Thanks in advance:smile::redface:
 
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f(x+h) = -x-h
 
blue_leaf77 said:
f(x+h) = -x-h
But how does that work? Why it isn't -x+h ?:oldconfused:
 
rishi kesh said:
But how does that work? Why it isn't -x+h ?:oldconfused:

Try ##x = 0## and see what you get.
 
PeroK said:
Try ##x = 0## and see what you get.
Hey! I think i got it!
When, f(x)= x^2
f(x+h)= (x+h)^2
If, f(x)= -x
f(x+h)= -(x+h)
= -x-h
Is this right?
 
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rishi kesh said:
Hey! I think i got it!
When, f(x)= x^2
f(x+h)= (x+h)^2
If, f(x)= -x
f(x+h)= -(x+h)
= -x-h
Is this right?

Quite right.
 
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