My Math Forum so many errors...derivative

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 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
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 Originally Posted by Bobbyjoe 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?
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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