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# Differentiation watch

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1. 1. find the gradient of

x^2 + y^2 = 9 at the points where x=1

2. find d^2y/dx^2 as a function of x if siny + cosy= x

Thanks
2. 1. At x=1, 1+y^2=9 --> y=sqrt(8), -sqrt(8)
2x + 2y.y` = 0 --> y`=-x/y
3. for 2, y`.cosy - y`.siny=1 --> y`=1/(cosy - siny). So y``=-(y`.-siny - y`.cosy)/(cosy - siny)^2. --> y``=y`(siny + cosy)/(cosy-siny)^2
--> y``=y`.x/(cosy-siny)^2
You simplify it further, it gets messy and i dont feel like typing.

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Updated: January 28, 2005
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