My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum

LinkBack Thread Tools Display Modes
November 29th, 2012, 06:34 AM   #1
Joined: Feb 2010

Posts: 6
Thanks: 0

Fundamental Derivative question

I know very well, How to derivate given function.
What I would love to know is Why we derivate? and what do we exactly get after differenciating?

Well, What I know is by derivating we can get slope of the tangent of the given point of graph. But then immediate next question would be, what is use of it?

lastly, the regular differenciation formula says, f'(x) = lim h->0 (f(x+h)-f(x)/h)

Why only limit of that equation is derivative and not every other limit is a derivative.

My questions are amateur I am aware of that but its the fundamental knowledge I want to have
thapchi is offline  
November 29th, 2012, 08:48 AM   #2
Joined: Jul 2012
From: Turkey, Zonguldak

Posts: 18
Thanks: 0

Re: Fundamental Derivative question

(f(x+h)-f(x))/h gives us the slope.
Let's see how it works: We have two points, (x, y) and (x+h, y). In functions graph, we use the f(x) value for y. So, our points are these: (x, f(x)) and (x+h, f(x+h)).
The slope of the line which contains these number is m=(f(x+h)-f(x))/h.
Why we take the limit when h approaches 0?
Well, we want to know the slope at any point. The equation gives us the slope in range [x, x+h]. We have to narrow the range, so that we can find the slope. However, we can't take h is equal to true because it's the denominator. So, we take the limit when h goes to 0.
I wish it helps.
kcancelik is offline  
November 30th, 2012, 05:53 AM   #3
Joined: Feb 2010

Posts: 6
Thanks: 0

Re: Fundamental Derivative question

Well, Thank you for explanation but I would like to know, Why we calculate slope of tangent
What can we achieve by calculating slope of tangent.
Well, Additionally, Why do we treat only that formula as the formula of calculating derivatives and not any other limit based function.

I am sorry if my questions are too basic, I know how to 'solve' this stuff, But I am curious about WHY we do all that...

Please help me understand fundamental logic behind them.

Thank you.
thapchi is offline  
November 30th, 2012, 11:18 AM   #4
Math Team
Joined: Sep 2007

Posts: 2,409
Thanks: 6

Re: Fundamental Derivative question

It would be better to actually take a Calculus course!

Remember that Newton (and Leibniz) first developed Calculus because of a fundamental "paradox" in gravitational theory. That is, if the gravitational force on an planet depended (as Newton suspected) on the distance then, since at any given instant the planet has a specific distance from the sun, then the force has a specifi value at that given intstant. Now, F= ma so a= F/m is the acceleration at that instant. But, while we are comfortable with the idea of an acceleration or velocity at a given instant, now, at that time the only possible concepts of acceleration and velocity were "average" acceleration and speed- change in speed or distance divided by change in time. If there is no change in time, there cannot be any motion and so no speed or acceleration.

Yet, we are asserting that the sun's gravity exerts a certain force on a planet, and so gives it a specific acceleration, at a give instant. How can that be? In order to make sense of that, we must have a way of defining rate of change at a give instant. And that is the idea of the "derivative". It is the rate of change of a function, f(x), at a given value of x rather than an average value.
HallsofIvy is offline  

  My Math Forum > College Math Forum > Calculus

derivative, fundamental, question

Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
Derivative question limes5 Calculus 4 April 16th, 2013 01:42 PM
Fundamental LA Question chomool Linear Algebra 1 February 17th, 2013 01:49 PM
fundamental question gaussrelatz Calculus 1 October 26th, 2011 12:27 AM
Fundamental and trivial question on triangle inequality. ChessTal Algebra 6 August 15th, 2011 06:18 PM
fundamental question gaussrelatz Algebra 1 December 31st, 1969 04:00 PM

Copyright © 2019 My Math Forum. All rights reserved.