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Difference between partial derivative and implicit differentiation

Anonymous Fri 01 Jan 23:33:43 2021 No.12533874 View Reply Original Report

Quoted By: >>12533878

I know you guys will probably laugh at me but im self-studying math before i start uni and i know its slightly different by the math procedure. But in leynman terms what is happening to the function that makes these two different concepts.

Anonymous

Anonymous Fri 01 Jan 2021 23:34:21 No.12533878 Report

Quoted By:

>>12533874
>layman terms

Anonymous

Anonymous Fri 01 Jan 2021 23:53:08 No.12533932 Report

Quoted By: >>12533954

They are two entirely different things so im not sure what youre confused about
Implicit differentiation:
Equation f(x,y) = 0 implicitly defines a function y=g(x). Find g'(x)
Partial differentiation:
Function in 2 arguments z=f(x,y) find lim (f(x+dx,y) - f(x,y)) / dx
And similiarly for y

Anonymous

Anonymous Fri 01 Jan 2021 23:56:53 No.12533944 Report

Quoted By: >>12533954

implicit differentiation as you have learned it is probably in terms of one variable. so you have a variable x, and then you have a function y=y(x) where y is a function of that x.
so you just want to find out dy/dx (the derivative of y with respect to x)

partial derivatives are used when you have a function of multiple variables. such as F(x,y). where F is a function of both x AND y.
so you have gone from a 1-D line (in 2-D space) to a 2-D plane (in 3-D space). this adds a lot of possibilities for how it behaves!
the idea is then to examine the function's behaviour in one direction at a time - because they may well be different
how does F behave as it moves in the x direction? and how does F behave as it moves in the y direction?
we call these the partial derivative of F (with respect to x), and the partial derivative of F (with respect to y)

Anonymous

Anonymous Fri 01 Jan 2021 23:58:48 No.12533954 Report

Quoted By:

>>12533932
i dont know kinda regret making this thread just seems weird how one time youre holding lets say y constant and with another differentiate one but end up isolating another in anyways jsut seems like they both should be linked in some way
>>12533944
thanks this helps but i guess the best way for me to understand maths is to always think of it in terms of a real life example like where are the real world applications where these two problems would differ.

Anonymous

Anonymous Sat 02 Jan 2021 15:11:39 No.12536413 Report

Quoted By:

the reason you are confused is because the highschool level calculus you are learning is not mathematics: it's algorithms. understanding the connection between algorithms requires an understanding of the deeper mathematics, which you have not yet learned, and which your curriculum is likely unable to provide at your current level of education.

tl;dr there is no accurate, easy, satisfying answer.

Anonymous

Anonymous Sat 02 Jan 2021 16:08:13 No.12536542 Report

Quoted By:

Partial differentiation holds one variable constant.

Implicit differentiation defines one variable as a function of the other.

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