/sci/ - Science & Math » Thread #11090671

102KiB, 1541x674, 34432322.png

View Same Google iqdb SauceNAO

I don't get it, why does he multiple by dx like that

Anonymous Fri 25 Oct 17:24:35 2019 No.11090671 View Reply Original Report

Quoted By: >>11090682 >>11090711 >>11090727

Isn't the reason why the dx goes away the fact that you factor the dx and then cancel it with the denominator. The the other dx goes away when we take the limit as dx -> 0?

Also why not use delta x and delta y, I thought we weren't supposed to treat dy/dx as a fraction

I don't get it, I mean he then concludes that it is equal to the derivative of x^2. But then that mean that delta x went to 0. How can you multiple 2x by delta x in that case? Please help I am trying to have an intuitive understanding of this and it has backfired.

https://youtu.be/S0_qX4VJhMQ?t=200

Anonymous

Anonymous Fri 25 Oct 2019 17:27:22 No.11090682 Report

Quoted By:

>>11090671
because he made x=the length of a side bigger by dx and if you look at the size of the enlarged square the two strips have width dx

Anonymous

Anonymous Fri 25 Oct 2019 17:38:52 No.11090711 Report

Quoted By:

>>11090671
df/dx=2x is a derivative of f, while df=2x dx is called a differential of f. Differentials are defined using the derivative, so df = (df/dx) dx, where the df/dx in parentheses is the actual derivative. Using primes to avoid ambiguity, f'=2x, and the differential is defined as df=f' dx. The differential represents the best linear approximation to a finite change in f with a finite change in x. At a given x value, you can plug in a number for the change dx at that x, and you will get a linear approximation for the change in f. For instance, plugging in x = 4 and dx = 0.5, I find that a linear approximation for a change of 0.5 in the function f=x^2 at the value x=4 is df=2*4*.5 = 4. The actual change is 4.5^2-4^2 = 4.25, so clearly there is some error. In the limit as my dx gets smaller and smaller, the change df gets more accurate, or in other words the error goes to zero.
There is no actual "multiplication/division by dx," there just appears to be because differentials and derivatives are closely linked, despite being somewhat different concepts.

Anonymous

Anonymous Fri 25 Oct 2019 17:45:20 No.11090727 Report

Quoted By:

>>11090671
df = f'(x) dx => df/dx = f'(x)

Anonymous

Anonymous Sat 26 Oct 2019 02:28:49 No.11091927 Report

Quoted By:

He basically said df=f(x+dx)-f(x), then expanded because f(x) =x^2. X^2 cancels, 2x*dx doesn't, dx^2 is too small to care about. That's the intuitive but wrong way of thinking about df, but it gets the point across

Capcode	All Only User Posts Only Moderator Posts Only Admin Posts Only Developer Posts
Show Posts	All Only With Images Only Without Images
Deleted Posts	All Only Deleted Posts Only Non-Deleted Posts
Ghost Posts	All Only Ghost Posts Only Non-Ghost Posts
Post Type	All Only Sticky Threads Only Opening Posts Only Reply Posts
Results	All Grouped By Threads
Order	Latest Posts First Oldest Posts First

Your latest searches