a. 9 choices for first digit (can't be 0), 9,8,7 etc for next digits
total = 9*9*8*7*6*5*4*3*2*1=9*9! = 3265920
b. 9 choices for first digit (can't be 0), 10 for each subsequent digit
total = 9 * 10^9 [9 other digits]
i'm sure there are good explanations online
while i haven't rly looked at it in a while i'm fairly sure partial derivative is just differentiating with respect to a certain variable and allowing all the other variables to act like constants