Could it be impossible to find derivative by basic definition?

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Homework Help Overview

The discussion revolves around finding the derivative of the function F(x) = 5x / (1+x^2) using the basic definition of a derivative. The original poster expresses difficulty in applying the definition in a specific form and questions the feasibility of solving similar equations.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the equivalence of different forms of the derivative definition and the challenges faced in manipulating these forms. There is mention of difficulties in canceling terms and recalling previous knowledge related to quadratic equations.

Discussion Status

The conversation is ongoing, with participants exploring different interpretations of the derivative definition. Some guidance has been offered regarding the basic definition, but no consensus has been reached on the specific challenges presented.

Contextual Notes

The original poster indicates a struggle with the mathematical manipulation required for the derivative, particularly in the context of their prior knowledge of quadratic equations. There is also a mention of a desire to close the topic, which is met with resistance from another participant.

Stramonium
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(I am sorry, totally forgot about solving quadratic equations, close the topic please)

Homework Statement



Finding derivative of the equation like F(x) = 5x / (1+x^2) by definition (ƒ(a+h) - f (a))/h is easy (point 2;2), but I got really stuck in finding a way to solve it by basic definition ( f(y) - f(a) )/( x - a ) :(

It seems to me there are much more such equations. Is there any way to do it?
 
Last edited:
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Isn't that the same thing?
As far as I know, the basic definition of derivative is:
23b7112ec7aa5d19157cf84bd3b392e8.png
 
The same, I just had difficulties with canceling equation derived from y - y1 / x - x1, because I totally forgot about solving quadratic equations:( It seemed strange to me on that moment that I could solve the (f(h) - f(a)) / a, but not another form:) Close the topic please.
 
Topics are not closed without a good reason.
 

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