January 3rd, 2009, 10:26 AM  #1 
Newbie Joined: Jan 2009 Posts: 1 Thanks: 0  Chain rule questoin
Hello all, I'm stuck on a problem and I'm hoping someone can help. Here is the problem: If y = f((x^2 + 9)^1/2) and f '(5) = 2, find dy/dx when x = 4. Here is what I have tried so far. I know that dy/dx = dy/du * du/dx. If u = (x^2 + 9)^1/2, then du/dx = x/(x^2 + 9)^1/2. so... 2 = dy/du * x/(x^2 + 9)^1/2 If I substitute x = 5, then... 2 = dy/du * 5/(34)^1/2 This doesn't seem right. I think I'm going down the wrong path to solve this one. Can anyone help me with this problem? Thanks. 
January 3rd, 2009, 06:04 PM  #2 
Senior Member Joined: Dec 2008 Posts: 251 Thanks: 0  Re: Chain rule questoin
Remember that when , , which is not necessarily equal to .

January 4th, 2009, 11:22 AM  #3 
Member Joined: Dec 2008 From: Washington state, of the United States Posts: 37 Thanks: 0  Re: Chain rule questoin and , find dy/dx when x = 4 Let x = 4 since f'(5) = 2: 

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