November 30th, 2017, 07:00 PM  #1 
Newbie Joined: Nov 2017 From: California Posts: 1 Thanks: 0  Second derivative help
I figured out the first derivative, and I know you have to use the quotient rule to get the second, but I get lost somewhere during the quotient rule.

November 30th, 2017, 07:13 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 1,785 Thanks: 920 
$y = x \sqrt{3x}$ $y^\prime = \sqrt{3x}  \dfrac{x}{2\sqrt{3x}}$ $y^{\prime \prime} = \dfrac{1}{2\sqrt{3x}}  \dfrac 1 2 \left(\dfrac{(1)(\sqrt{3x})(x)\left(\dfrac{1}{2\sqrt{3x}}\right)}{3x}\right)$ and I leave simplifying the algebra to you 
December 9th, 2017, 05:45 AM  #3 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,966 Thanks: 807 
If you don't like to use the quotient rule, or as a check, you can write the denominator with a negative exponent and use the product rule. For example, we can write $\displaystyle \frac{x}{2\sqrt{3 x}}$ as $\frac{1}{2}x(3 x)^{1/2}$. By the product rule, the derivative is $\frac{1}{2}\left((3 x)^{1/2}+ x(3 x)^{3/2}(1)\right)$. If you want to put the answer back into the same form as the problem was given write those negative exponents as fractions with common denominator $(3 x)^{3/2}$: $\frac{(3 x)}{2(3 x)^{3/2}} \frac{x}{2(3 x)^{3/2}}= \frac{3 2x}{2(3 x)^{3/2}}= \frac{3 2x}{2(3 x)\sqrt{3 x}}$ 
December 25th, 2017, 07:47 AM  #4 
Newbie Joined: Dec 2017 From: Netherlands Posts: 2 Thanks: 0 
Here is a proposed solution to your problem


Tags 
derivative 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
relationship between derivative of function and derivative of inverse  daltyboy11  Calculus  2  July 10th, 2014 06:57 PM 
problem with simplification when taking the derivative of a derivative  lackofimagination  Calculus  1  July 6th, 2014 08:05 PM 
Derivative of x^1x  azerty  Calculus  6  April 10th, 2013 10:10 AM 
Lie Derivative (directional derivative proof)  supaman5  Linear Algebra  0  November 26th, 2012 10:14 AM 
Find derivative of f(x)=(3+x)/(2x) using def. of derivative  rgarcia128  Calculus  4  September 24th, 2011 05:07 PM 