Saturday
April 19, 2014

Homework Help: differentiation

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

by determining :

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

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:

http://en.wikipedia.org/wiki/Hyperreal_number

Answer this Question

First Name:
School Subject:
Answer:

Related Questions

Calc, Implicit Differentiation - Regard y as independent variable and x as ...
Calculus - Use implicit differentiation to find dy/dx if cos xy = 2x^2 - 3y. I'm...
Calculus (repost) - Use implicit differentiation to find dy/dx if cos xy = 2x^2...
bobpursley,math - about this problem , I figured it out and i did get the answer...
Math differentiation - Can somebody please check these over for me? I really ...
Calculus 12th grade (double check my work please) - 1.)Find dy/dx when y= Ln (...
Ap Calc AB - Determine (dy/dx) using implicit differentiation. cos(X^2Y^2) = x I...
Calculus (Please check my work!) - Suppose that y = f(x) = x^2 - 4x + 4. Then on...
math - i need some serious help with limits in pre-calc. here are a few ...
maths - Choose the option that gives the solution of the initial-value problem ...

Search
Members