January 29, 2015

Homework Help: differentiation

Posted by Emma on Friday, May 25, 2007 at 7:25am.

by determining :

lim f(x+h)-f(x)
h->0 ---------------

show that if f(x)=2x^2+2 then dy/dx=4x.

i figured out that f'(x) is 4x...but i am confused about what to do next...someone help?

"i figured out that f'(x) is 4x..."

That's the answer! dy/dx is just a notation for the derivative. If the function f(x) is dentoted by y, then

f(x+h)-f(x) can be called Delta y (i.e. a change in y) and h is, of course, a change in x, which we can denote as Delta x. So, the ratio

[f(x+h)-f(x)]/h can also be written as:

Delta y/Delta x

The derivative is obtained by taking the limit Delta x--->0. The notation for this limiting case is dy/dx

This notation dates back from the time before limits were invented. dy and dx were taken to be infinitesimal quantities, i.e. smaller than any positive number, yet larger than zero. When mathematics was further developed in the 19-th century it was found that infinitesimal numbers were an ill defined concept and limits were invented to do calculus.

The notation dy/dx for the derivative was kept but you could no longer interpret it as a ratio of two well defined quantities dy and dx.

However, in the 1960s Abraham Robinson showed how one can rigorously define infinitesimal numbers, see here:

Answer this Question

First Name:
School Subject:

Related Questions

Math - I am confused with rule of pattern 1,3,6, I figured out 10 is the next ...
calc - need to find: lim as x -> 0 of 4(e^2x - 1) / (e^x -1) Try splitting ...
calculus - ratio test - infinity of the summation n=1: (e^n)/(n!) [using the ...
calc bc (condensed - is the limit as x approaches 0 of sin3x over 3x equal to ...
math - lim (2x^2+3x-2)/ (2x-1) the lim is x->1/2 [ans:5/2 but i get 3/2) can ...
math - solve lim (5000t^2)/ (t+2)^2. the lim is t->infinity. can someone show...
Calculus - Find the limit. lim 5-x/(x^2-25) x-->5 Here is the work I have so ...
Calc. Limits - Are these correct? lim x->0 (x)/(sqrt(x^2+4) - 2) I get 4/0...
calc - Are these correct? lim x->0 (x)/(sqrt(x^2+4) - 2) I get 4/0= +/- ...
TRIGONOMETRY - 3. The rectangular coordinates of a point are given. Find the ...