Mid Semester Calculus 2010

1. Determine the first derivative or (x) of the following functions.

2. Company Maker processor (Intel) is planning to make a serial number on each unit of production for 1 decade, namely the 5 characters in the first 5 years and 7 characters in the last 5 years. If any numerical starts with 2 letters (Capital), terminated by 2 lowercase letters, and the rest of the middle character is numeric, with each uppercase characters may only be repeated 1 times, lowercase characters and numbers only may be repeated 2 times. How many units can be produced in a decade that a character first begins with the letter ends with a consonant or a vowel in his last character, or filled by prime numbers on the character of the score, but not all three?

3. Due to security reasons and also the large number of users resulting in limited ability of storage to store character password, the password of a logged on computer systems must be five characters in length is determined. Each character may contain letters (key sensitive) as well as numbers. When each character can only be repeated a maximum of two times, How many passwords that can be made ​​for a login first two characters begins with the letter or terminated by the numbers on the two last character or characters the middle (3rd) is a number, but not all three ?

Please can you answer in the comments ... : D