Add instructions and sample cases. Beginners might have a hard time knowing what "flattening a list" means.

Done. Final testing takes values from random.randint().

Not really a grave issue, but you typed in

poly_derivative([1, 2] ) = [2]
poly_derivative([9, 1, 3]) =  [1, 9]

instead of

poly_derivative([1, 2] ) = [2]
poly_derivative([9, 1, 3]) =  [1, 6]

in your instructions.
I was confused at first (why is 9x the derivative of 3x2?!), but, yeah. Although test case resolves this.

The instruction is unclear

The example rendered as

123
123

123

instead of something like

123
123
123