So I just discovered how to make Integration and Derivatives in roblox so i thought ill share it with yall, if anyone needs it

# Derivative

- Create a function… of course

## info

._.

```
function Derivative()
end
```

- Add a number and a function argument

## info

# f’(x)

here `x`

is our number argument and `f`

is the function arg.

you can name the arguments anything but you have to assign the names everywhere

```
function Derivative(x: number, f: ())
end
```

- Create a really small constant

## info

The smaller the constant, the bigger the accuracy and

```
function Derivative(x: number, f: ())
local C = 1e-10
end
```

- Calculate the slope of
**f**from**x**to**x+C**

## info

This is a bit confusing so please just CTRL+C, CTRL+V it if you dont understand ><

```
function Derivative(x: number, f: ())
local C = 1e-10
local slope = ( f(x+C) - f(x) )/C
end
```

- And lastly, return the slope
**Results:**

```
function Derivative(x: number, f: ())
local C = 1e-10
local slope = ( f(x+C) - f(x) )/C
return slope
end
```

# Integration

- Create a function with 2 number and 1 function argument.

## info

;-;

```
function Integral(x: number, y: number, f: ())
end
```

- Create a small constant and a zero constant.

## info ❗

If the constant is smaller than `1e-6`

then it might ~~blow up your pc~~ crash your game.

```
function Integral(x: number, y: number, f: ())
local C = 1e-5
local a = 0
end
```

- Make a
`for loop`

starting at**x**, ending at**y**and grows by**C**

## info

shorty, `for x,y,C do`

```
function Integral(x: number, y: number, f: ())
local C = 1e-5
local a = 0
for i = x,y,C do
end
end
```

- Insert
`f(i)*C`

into the loop (adding it to`a`

)

## info

f(i)*C is a thin line under the curve. All of those make up the integral.

```
function Integral(x: number, y: number, f: ())
local C = 1e-5
local a = 0
for i = x,y,C do
a += f(i)*C
end
end
```

- And lastly, return
`a`

:)) **result:**

```
function Integral(x: number, y: number, f: ())
local C = 1e-5
local a = 0
for i = x,y,C do
a += f(i)*C
end
return a
end
```

**NOTE:** *i didn’t test this in every way i wanted to. It might have bugs or might not even work. I just learned Integration and Derivatives. Also… Integration is 5 decimals accurate*