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I've been recently thinking about derivative and it's applications.

Let's say Y=3x

When X = 1, Y=3

wHEN X = 2, Y = 6

When X = 3, Y = 9

Dy/Dx is the rate of change in Y with respect X, it is 6-3/2-1 =3/1 = 3

and the derivative is 3.

Let's Y = (X)^2

When X = 1, Y=1

When X = 2, Y = 4

When X = 3 , Y=9

When X = 4 , Y = 16

Dy/dx = 4-1/2-1 = 3/1 = 3

Dy/dx = 9-4/3-2 =5/1 = 5

Dy Dx = 16-9/4-3=7/1 = 7

So the rate of Change is not constant.

When you derive you get 2x

When you plug values in the function, you get different values from the the rate of change, Where is my mistake?

Thanks.