Question

What is a partial derivatives?

Answer 1

a function of two or more variables with knowledge of one variable, the other(s) being treated as constant.

Answer 2

We meet again... :/
Given a function of several variables, the partial derivative of the function with respect to one of the variables is the function differentiated along that variable while holding all others constant.

The practical upshot of which is... you just differentiate with respect to one variable, and pretend every other is a constant.

Answer 3

Give me an example of function given the partial derivation of it. :)

Answer 4

sounds like an essay question :/

Answer 5

The word is 'differentiation' :/
So.. let's have a function
\[\huge f(x,y)=x^4y + x\cos \ y\]
If we were to take its partial derivative with respect to x, pretend y is some constant...
\[\huge \frac{\partial}{\partial x}f(x,y)=4x^3y+\cos \ y\]

Answer 6

so what amistre64? :) is that a problem?

Answer 7

TERRENZ WAG MO NA SAGUTIN :) THANKS NA LANG.

Answer 8

^Translation:
"TERRENZ DON'T BOTHER ANSWERING :) THANKS ANYWAY."

Answer 9

We need to think and analyze definitions in a way that we can master the subject...

Answer 10

its a problem if you are just using this site to get others to do your work for you :)

Answer 11

it might be better if you offered a multivariable function, that others can walk you thru. is what im thinking is all

Answer 12

Okay. I'm sorry for what I've said earlier. Sorry

Answer 13

The first question is why don't we vary all the variables at the same time? in other words take the rate of change at the same time

Answer 14

now this question is a key for many calculus subjects and topics

Answer 15

sorry :)

Answer 16

should i continue in exploring the definition of partial derivative...

Answer 17

@mathsmind
Yes :D
I'm learning.

Answer 18

so i don't waste my time typing to myself hehehe

Answer 19

all of this is based on the fact that each variables behave in different manners, in terms of a speed of a variable, some variables are slow and some of them are fast, so this requires dealing with such a function in a convenient way

Answer 20

I can't post what I wanted to ask.

Answer 21

Imagine u have 2 kids one is slow and the other one runs fast, how would u deal with such a situation?

Answer 22

see that draw button down there? click it and draw the equation, if you have one.
I'll see if I can put it up more nicely using the equation editor.

Or, better yet, click the equation editor, and explore it.

Answer 23

saying "slow kid" is not politically correct these days ;)

Answer 24

heheheh ok ur funny i admit

Answer 25

it seems ur suffering a lot these days

Answer 26

let me say a calm kid and a naughty one

Answer 27

Sorry again @amistre64

Answer 28

Or a kid who runs more quickly than the other. At least you didn't explicitly say slow kid.

Answer 29

mishy, as long as you are learning something, its fine ;)

Answer 30

well this is just an analogy i was trying to make it similar to slow variables and fast variables, after u get my concept u may use ur own analogy

Answer 31

now to cope with such situation with slow and fast kids u'll end up with infinite ways of controlling such a conflict...

Answer 32

one way is to keep some of them quite and deal with the other ones

Answer 33

now this method is efficient, here comes the basic concept behind partial derivative, because one might ask what is the difference between PD and MVC?

Answer 34

so due to the fact that one variable rate is faster than the other we deal with each variable one at a time, similar to the superposition principle, and this is why PD plays a good role in Vector Calculus...

Answer 35

MVC?

Answer 36

multi variable calculus get used to my terms hehehe

Answer 37

right then.

Answer 38

and this is why partial derivatives can also be taught at single variable calculus according to some authers

Answer 39

despite the fact it is a multivariable function

Answer 40

if we were to differentiate all the terms like i did and others did in proving kepler's 3 laws of planetary motion, it is a long process...

Answer 41

but really what does it mean differentiating one variable of a multivariable function and keeping another variable constant?

Answer 42

@mathsmind can you help how to solve a function using chain rule in partial derivatives?

Answer 43

let's get a bit formal, i was trying to put this in an informal way

Answer 44

everyone here can solve PD and help

Answer 45

well u might need to use product rule as well, chain rule, Q rule, D-operator, reduction formulas of diff...etc

Answer 46

u might need to use all those methods at the same time, so not just the chain rule...

Answer 47

Its confusing when it comes to partial derivatives when I have to use the different chain rule.

Answer 48

what do we mean by one veritable is faster than the other? well we may visualize that in terms of the big O, or in simple words if we use a variable in an exponential or the simple linear form, which one would be faster than the other?

Answer 49

nothing is confusing unless we confuse ourselves... so psychologically stop convincing yourself about being confused, in other words fight confusion by focusing ... this is the battle of ur mind...

Answer 50

Thanks for that inspiring message :D

Answer 51

u may submit ur question and u'll see anyone here can solve the question in a passionate way...

Answer 52

Do you know the contour plotting in a three dimensional into two dimensional?

Answer 53

some think that differentiation is all about finding a tangent of a line, hence partial derivative i finding tangents of a plane, however such a thought although its true to a certain extent but that would never be the complete vision at all, due to the fact that differentiation also deals with the dynamic world...

Answer 54

tangent of a curve*

Answer 55

yes what about it all u need a simple transformation...

Answer 56

Simple transformation? how?

Answer 57

how would i model the real world using partial derivative? how do i know i need to use and ODE or PD?

Answer 58

No. Its not that. anyway, thanks :)

Answer 59

sorry i am trying to finish up explaining what PD is

Answer 60

look dear one topic at a time...ok

Answer 61

okay. :)

Answer 62

consider the electromagnetic field or even a VCO of let's say 10 transistors, would partial derivative be of any use?

Answer 63

in some circuit analysis we need to make abstract assumptions, which means we need to assume some parts of the circuit are constant and others are varying, or we may assume some parts are switched off at the same time the other parts are functioning

Answer 64

so here maths plays a major role especially when we use capacitors and inductors that brings us back to the world of calculus

Answer 65

in summary in order to model the real world using PD, this happens in modeling a multi dynamic system, were assumption are made for constant variables and varying variables in order to model the real world application that simplifies destining a prototype for the sake of production, this is one view of how to see PD.