The partial derivative of the sum with respect to `x`

or `y`

equals 1 (i.e. if you only see addition, the result be always 1):

The partial derivative of `x`

multiplied by `y`

, with respect to `x`

or `y`

, equals the other output (i.e. if you only see multiplication between `x`

and `y`

, they exchange their values with each other, always):

The partial derivative of `max()`

of 2 variables with respect to either of them is `1`

if that variable is the biggest, otherwise `0`

:

The derivative of the `max()`

of a single variable `x`

equals `1`

if `x > 0`

, otherwise `0`

:

- 1 if
`x`

>`y`

else 0 - 1 if
`x`

> 0 else 0

The derivative of chained functions equals the product of the partial derivatives of subsequent functions:

# Gradient

The gradient is a vector of all possible partial derivatives (i.e. the inverted triangle is just the notation/symbol for the “things” where the red arrow is pointing):