# The Chain Rule

Published on: Fri Dec 05 2008

Practicing problems from UCDavis. Problem 1 Problem 2 Note to Self: Square roots. To find the derivative of a square root, change the square root into a fraction and proceed, using the exponent rule. Ie. The derivative of the square root of x is 1/2x-1/2 Problem 3 According to the shown solution this answer is wrong. I should have included (-4+35x4) inside of the exponent “29”. I don’t know why I should do this. Is it because a simple version of this might look like 3(x5)2(x4)? I believe with that sort of problem I could write out 3(x5)(x4)2 and if I solve either one of those two I would get the same answer. Lets try that: Let x = 2 3(x5)2(x4) 3(32)2(14) 3(1024)(14) 43008 3(25)(24)2 3(32)(14)2 1806336 That’s not right either. I’m going to have to do some research on this. And in the mean time make a mental note, to move the values bracketing the (u) formula to the end! Solved; See Problem 6 Problem #4 OK… So I answered this one wrong as well. (The correct answer is shown though..) This time I should not have pulled g’(x) inside of the exponent, like I needed to in problem #3. So what is going on here? How to do I handle exponents? Solved; See Problem 6 As a side note. I’ve learned how to “Align along = sign” How nice! Problem #5 Ok. This one immediately threw me for a loop with the division AND the exponent. First things first, I was able to reduce u, leaving the inner function division free but with negative exponents. After that it was smooth flowing, except by the end of my problem, I still have three pesky negative exponents which I need to simplify out of existence. Problem #6 I got this one right! And it was EASY! Dxy Sin(x) = Cos(x) I believe I’ve also solved the exponent trouble I was having. The trick is to simplify first when u is still a variable, and then once simplified completely, replace u