# How to find partial derivatives in matlab

## Partial derivative

Ex: z = x² + 4y³

-> dz / dx -> it is resolved for x

z´ = 2x

According to y = z´ = 12y²

Example 2:

z = 4x1²x2 + x1 x2 x3 + x2 - x4

If one solves for x1 to -_> dz / dx1

This results in the following:

z´ = 8x1 x2 + x2 x3

You see 4x1² becomes clear 8x1 and x1 x2 x3 becomes only x2 x3,

since x1 is derived from x1 x2 x3 as a constant factor but is part of a multiplicative and thus the rest remains

As with every function, the most important thing here is to be able to calculate and evaluate extreme points.

As with a normal derivation, one speaks here of a necessary one

and sufficient condition.

Hence: z = f´x or f´y (x, y) at xo / yo = 0

Namely all 1st derivatives of f, i.e. all representations of the area for each variable

-> All methods are used for the solution, which are also used for the solution of lin.

If you have found a candidate for the sufficient conditions, you put this in as usual

f´´x (xo, yo) <0 / f´´y (xo, yo) <0 = maximum

> 0 = minimum

The partial integration finds practical application in the area of ​​the long range method and its function and derivation