November 28th, 2010, 04:35 AM  #1 
Senior Member Joined: Oct 2009 Posts: 895 Thanks: 1  Questions in derivatives
Hi all what is the derivative of ysin(1/y)=1xy my answr derivative (ysin(1/y)= derivative (1xy) 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, 06:55 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, 07:49 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, 12:31 PM  #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 is 

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