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 November 28th, 2010, 03:35 AM #1 Senior Member   Joined: Oct 2009 Posts: 895 Thanks: 1 Questions in derivatives Hi all what is the derivative of ysin(1/y)=1-xy my answr derivative (ysin(1/y)= derivative (1-xy) y.cos(1/y).(-y^-2) + sind(1/y).y' = -xy'-y y'(-y/ycos(1/y).(-y^-2)+x) ------------ find dr/dQ cosr + cosQ=rQ my answar derivative(cosr ) + derivative( cosQ) = derivative (rQ) -sinr + cosQ = r+sinQ plese (correcrt to me and explaine whre I do mistake )
 November 28th, 2010, 05:55 AM #2 Senior Member   Joined: Nov 2010 From: Staten Island, NY Posts: 152 Thanks: 0 Re: Questions in derivatives Corrections are in bold: y.cos(1/y).(-y^-2)y' + sin(1/y).y' = -xy'-y (-sinr)r' -sin Q= r+Qr'
 November 28th, 2010, 06:49 AM #3 Senior Member   Joined: Oct 2009 Posts: 895 Thanks: 1 Re: Questions in derivatives in question 1 why you put y' after cos(1/y).(-y^-2) ?
 November 28th, 2010, 11:31 AM #4 Senior Member   Joined: Nov 2010 From: Staten Island, NY Posts: 152 Thanks: 0 Re: Questions in derivatives If y=f(x), then when differentiating implicitly, you always follow a derivative involving y by dy/dx. This is due to the chain rule. For example, the derivative of $y^2$ is $2yy'$

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