My Math Forum Differentiation

 Calculus Calculus Math Forum

 December 31st, 2014, 05:44 PM #1 Senior Member   Joined: Sep 2013 From: Earth Posts: 827 Thanks: 36 Differentiation I'm given $\displaystyle y=\frac{cos2x}{1-sinx}$ to differentiate. My answer is $\displaystyle \frac{cosxcos2x-2(sin2x)(1-sinx)}{(1-sinx)^2}$ But the given answer is $\displaystyle -\frac{4sin(2x)-3cos(x)+cos(3x)}{2(sin(x)-1)^2}$.
 December 31st, 2014, 11:04 PM #2 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,950 Thanks: 1141 Math Focus: Elementary mathematics and beyond Post your work and we'll help you identify and correct any errors. Thanks from szz
 January 1st, 2015, 12:10 AM #3 Senior Member   Joined: Sep 2013 From: Earth Posts: 827 Thanks: 36 $\displaystyle y=\frac{cos2x}{1-sinx}$ $\displaystyle \frac{dy}{dx}=\frac{(1-sinx)(-2sin2x)-(cos2x)(-cosx)}{(1-sinx)^2}$ $\displaystyle =\frac{-2sin2x+2sin^22x+cosx(cos2x)}{(1-sinx)^2}$ $\displaystyle =\frac{(-2)(sin2x)\left [ 1-sinx \right ]+cosx(cos2x)}{(1-sinx)^2}$ $\displaystyle =\frac{cosxcos2x-2(sin2x)(1-sinx)}{(1-sinx)^2}$ The given answer is $\displaystyle -\frac{4sin(2x)-3cos(x)+cos(3x)}{2(sin(x)-1)^2}$
 January 1st, 2015, 09:43 AM #4 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,950 Thanks: 1141 Math Focus: Elementary mathematics and beyond The given answer is correct. Your mistake is in assuming $\displaystyle (-\sin(x))(-2\sin(2x))=2\sin^2(2x)$ Correct that, then use the identities $\displaystyle \cos(\theta)-\cos(\varphi)= -2\sin\left(\frac{\theta+\varphi}{2}\right)\sin \left(\frac{\theta-\varphi}{2}\right)$ and $\displaystyle \cos(\theta)+\cos(\varphi)=2\cos\left(\frac{\theta +\varphi}{2}\right)\cos\left(\frac{\theta-\varphi}{2}\right)$ to simplify further. Thanks from szz
 January 3rd, 2015, 08:31 AM #5 Senior Member   Joined: Sep 2013 From: Earth Posts: 827 Thanks: 36 What this symbol $\displaystyle \varphi$ means?
 January 3rd, 2015, 09:31 AM #6 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,671 Thanks: 2651 Math Focus: Mainly analysis and algebra It's a variable, phi, like theta is a variable.

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post Pudding Calculus 3 February 15th, 2013 04:25 AM maximia Calculus 4 January 31st, 2013 07:48 PM najaa Calculus 2 November 17th, 2012 10:11 AM gspimoli Calculus 1 November 12th, 2012 06:40 AM florian101 Calculus 1 December 22nd, 2009 06:42 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top