/sci/ - Science & Math

[Anonymous No.11248800]

f = f(x, y)

df = f(x + dx, y + dy) - f(x, y)
= f(x + dx, y + dy) - f(x, y + dy) + f(x, y + dy)- f(x, y)
= f_x.dx + f_y.dy

because evaluating the partial derivative at y+dy instead of y doesn't make any difference, right?

[Anonymous No.11248845]

Yep, taking the partial derivative wrt x at y+dy gives:

f_x(1 + dy/dx)

But since x and y are independent dy/dx = 0.

[Anonymous No.11249172]

>>11248845

wat?

[Anonymous No.11250377]

>>11248800
Think of [math]{\rm d} f[/math] as a basis (coordinate) free representation of [math]\mathbf{J}_f[/math]. I you *really* want to go the infinitesimal route, just disregard [math]{\cal O}(\delta x^2),{\cal O}(\delta y^2),{\cal O}(\delta x\delta y)[/math] terms.

[Anonymous No.11250380]

>>11248800
Made for BWC.

[Anonymous No.11250395]

[Anonymous No.11250408]

>>11248800
Holyshit this image is old, last time I saw it I was using modems to connect to the internet after stealing Deep freeze password from my mother notebook