May 9th, 2017, 12:05 PM  #1 
Member Joined: Feb 2017 From: henderson Posts: 36 Thanks: 0  so many errors...derivative
x/sin^2(x) x does not go with the 2 up like sin(x) you have to use quotient rule f'(x)g(x)g'(x)f(x)/(g(x))^2 f'= is 1 but g'? Little bit confused. Isn't it chain rule? Last edited by skipjack; May 10th, 2017 at 09:20 PM. 
May 9th, 2017, 12:14 PM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,806 Thanks: 1045 Math Focus: Elementary mathematics and beyond 
It's the power rule and the chain rule: $(\sin^2(x))'=2\cdot\sin(x)\cdot\cos(x)$.

May 10th, 2017, 09:04 AM  #3 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,160 Thanks: 866  Yes, it is. Let u= sin(x) so that g(u)= u^2. Then dg/du = 2u and du/dx = cos(x). By the chain rule, dg(u)/dx = (dg/du)(du/dx) = (2u)(cos(x)) = 2 sin(x) cos(x).
Last edited by skipjack; May 10th, 2017 at 09:22 PM. 

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