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May 1st, 2017, 08:46 AM  #1 
Newbie Joined: May 2017 From: Copenhagen Posts: 1 Thanks: 0  Differentiating x(t)
I'm having trouble with an entrylevel exercise in my differential equations class, and I feel very stupid as this shouldn't be too hard. I think I'm missing some basic knowledge about how to differentiate these kinds of problems. Here is a picture of the problem along with my thoughts: http://i.imgur.com/LIlv5fC.png I understand that I need to use the chain rule to differentiate, but I'm not sure how to apply it in this case. 
May 1st, 2017, 03:32 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 18,155 Thanks: 1422 
Make sure you know the product rule for differentiating a product. The derivative of $\text{x}^2\!$ with respect to $\text{t}$ is $2\text{x}\dot{\text{x}}$. You could differentiate the given solution and then multiply both sides by $\text{x}$, etc. 

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