what is differentiation???

Question

infact i have to present this topic...so do tell me..what is differentiation?why we use it???what type of formulas,we use...in differentiation??do tell me now!!1thank uuuuu!!! :)

Answer 1

(I assume you know what a function is....if not then email me and I'll explain that too.)

In a nutshell, differentiation is the process of finding the rate at which a function changes, which is called the derivative. It's usually written as f'(x), or dy/dx, or y'.

The goal of finding the derivative of a function is to find the function's slope (change in y over change in x) at every point.

The formal definition of a derivative of a function uses something called a limit.

Specifically, the derivative of a function at a particular x value (call it a) is defined as the limit as x approaches a of:

f(x) - f(a)
----------
x - a

But in practice, you almost never have to use limits; you just learn the rules.

Polynomial Rule:

One of the easiest rules is that, if you have a polynomial, for instance:

f(x) = 7x² - 3x + 7

Then the rule is that the derivative of:

axⁿ

is

naxⁿˉ¹

So:

f(x) = 7x² - 3x + 7
f'(x) = (2)7x²ˉ¹ - (1)3x¹ˉ¹ + (0)7
f'(x) = 14x - 3

Three other rules that are really useful are:

The Product Rule:

The derivative of the product of two functions is the first times the derivative of the second plus the second times the derivative of the first:

[f(x)g(x)] = f(x)g'(x) + f'(x)g(x)

Example:

x³ = x² × x

(x³)' = [x² × x]' = x²(1) + 2x(x) = x² + 2x² = 3x², which you can check using the rule above.

The Quotient Rule:

The derivative of the quotient of two functions is the quotient of (the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator), divided by the square of the denominator. (WHEW! The way I remember this is "Down-D-up minus Up-D-Down over Down-Down.):

[f(x)/g(x)]' = (g(x)f'(x) - f(x)g'(x)) / [f(x)]²

Example: x² = x³/x

(x²)' = [x³/x]' = (x(3x²) - x³(1)) / x² = (3x³ - x³) / x² = 2x³ / x² = 2x, which again you can check using the polynomial rule above.

The Chain Rule:

The derivative of the "composition" (f(g(x)) of two functions is the derivative of the outer function with the inner function plugged into it, times the derivative of the inner function:

[f(g(x))]' = f'(g(x))g'(x)

Example: x^4 = (x²)²

(x^4)' = [(x²)²]' = 2(x²)(2x) = 4x³, which you can check with the formula above.

That's a quick and dirty overview of the first semester of calculus.

It's also probably a little more than you can follow...don't worry about that. The important thing is the definition of the derivative and what it is used for. You asked for the formulas too, so I gave you the most basic ones.

Answer 2

dif·fer·en·ti·a·tion (dĭf'ə-rěn'shē-ā'shən) Pronunciation Key
n.

1.
1. The act or process of differentiating.
2. The state of becoming differentiated.
2. Mathematics The process of computing a derivative.
3. Biology The process by which cells or tissues undergo a change toward a more specialized form or function, especially during embryonic development.

Answer 3

basiclly in mathmatics differentiation is the act of carrying out a derivative problem.
in differentiation there are a lot of formulas to use.
basiclly there r som rulw , product rule and more.


but i wanna suggest u to get a better way of preparing a "paper" 4 it.

Answer 4

Basically differenciation is breaking down a large quantity or object into as small fragments as possible nd observing the properties of the smallest fragment

Answer 5

Why don't you research it yourself. If you have to present this topic, you should do the work yourself. PLUS most of these people will just google differentiation and find out what it is.... I'm sure you can just do it yourself.

Answer 6

differentiation is when when we compare positive and negative sides of a thing..we use it so whe cand tell wich thing is better[ for example when we compare 2 mobile phones] hope i helped u:)[ah..also there are different formulas , u can say 4 example that phone has a vga camera..but that one has a 3.1 mp one...oru can say "that phone differs from the other one by...]

Answer 7

Differential calculus is described here. http://en.wikipedia.org/wiki/Calculus