Could it be impossible to find derivative by basic definition?

In summary, the conversation is about solving quadratic equations and finding derivatives by definition. The person had difficulties with solving an equation using the basic definition and was wondering if there was another way to do it. The topic was then requested to be closed.
  • #1
Stramonium
2
0
(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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  • #2
Isn't that the same thing?
As far as I know, the basic definition of derivative is:
23b7112ec7aa5d19157cf84bd3b392e8.png
 
  • #3
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.
 
  • #4
Topics are not closed without a good reason.
 

Related to Could it be impossible to find derivative by basic definition?

1. What is the basic definition of a derivative?

The basic definition of a derivative is the instantaneous rate of change of a function at a specific point. It is represented by the slope of the tangent line to the curve at that point.

2. Why is it sometimes impossible to find a derivative using the basic definition?

It can be impossible to find a derivative using the basic definition if the function is not continuous or differentiable at the given point. This means that the function may have a sharp corner, a vertical tangent, or a discontinuity, making it impossible to find a unique tangent line.

3. Is it always necessary to use the basic definition to find a derivative?

No, it is not always necessary to use the basic definition to find a derivative. There are other methods, such as the power rule, product rule, and chain rule, that can be used to find derivatives of more complex functions.

4. Can a function have a derivative at some points but not at others?

Yes, a function can have a derivative at some points but not at others. This is because the function may be continuous and differentiable at certain points, but not at others. This is often the case for functions with sharp corners or discontinuities.

5. Are there any alternative methods for finding derivatives?

Yes, there are alternative methods for finding derivatives. Some of these methods include using the limit definition of a derivative, using the graphical interpretation of derivatives, and using numerical methods such as finite differences or Newton's method.

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