November 18th, 2012, 11:34 AM  #1 
Member Joined: Apr 2011 Posts: 47 Thanks: 0  Differentiating e
I have been given the equation y=xe^3x The answer is e^3x (1 + 3x) How? I thought maybe they are pulling down the 3x and and multiplying by 1, but why +1? 
November 18th, 2012, 11:53 AM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,164 Thanks: 472 Math Focus: Calculus/ODEs  Re: Differentiating e
We are given to differentiate: Using the product and chain rules, we find: 
November 18th, 2012, 11:58 AM  #3 
Member Joined: Apr 2011 Posts: 47 Thanks: 0  Re: Differentiating e
Oh I see. Thank you. Another similar problem is e^(1+3t)^2 The answer is 6(1+3t)*e^(1+3t)^2 I just am not understanding how to get the 6(1+3t). Thank you for the continued help. 
November 18th, 2012, 12:08 PM  #4 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,164 Thanks: 472 Math Focus: Calculus/ODEs  Re: Differentiating e
Using the chain rule, we find: 
November 18th, 2012, 12:56 PM  #5 
Member Joined: Apr 2011 Posts: 47 Thanks: 0  Re: Differentiating e
Ah, I see that we must split it up many times. Can you offer your help on this equation? y=x^2 * lnx and t^2 + 2lnt Thank you for helping. I am slowly understanding 
November 19th, 2012, 09:05 AM  #6  
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  Re: Differentiating e Quote:
Do you know the derivatives of and ? and t^2 + 2lnt Thank you for helping. I am slowly understanding [/quote]  

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