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November 28th, 2010, 04:35 AM   #1
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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 )
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November 28th, 2010, 06:55 AM   #2
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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'
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November 28th, 2010, 07:49 AM   #3
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Re: Questions in derivatives

in question 1

why you put y' after cos(1/y).(-y^-2)

?
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November 28th, 2010, 12:31 PM   #4
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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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