41059 ÷ 9 = 4562 R1
Alright, let's work through the division of 41059 by 9 step by step.

Step 1:
9 goes into 4 0 times with a remainder of 4.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 4 to get 4.
Bring next digit (1) of the dividend behind the 4 and repeat the process: 41 / 9

Step 2:
9 goes into 41 4 times with a remainder of 5.
Write down 4 as next digit of of the result. 
Result so far: 4
Subtract 36 from 41 to get 5.
Bring next digit (0) of the dividend behind the 5 and repeat the process: 50 / 9

Step 3:
9 goes into 50 5 times with a remainder of 5.
Write down 5 as next digit of of the result. 
Result so far: 45
Subtract 45 from 50 to get 5.
Bring next digit (5) of the dividend behind the 5 and repeat the process: 55 / 9

Step 4:
9 goes into 55 6 times with a remainder of 1.
Write down 6 as next digit of of the result. 
Result so far: 456
Subtract 54 from 55 to get 1.
Bring next digit (9) of the dividend behind the 1 and repeat the process: 19 / 9

Step 5:
9 goes into 19 2 times with a remainder of 1.
Write down 2 as next digit of of the result. 
Result so far: 4562
Subtract 18 from 19 to get 1.

The final result is 4562 with a remainder of 1.