MATH110 December 2013
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Find the derivative of with respect to at the point along the curve:
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If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!
Take the derivative using implicit differentiation and plug in the point. Don't forget to use a product rule on the right hand side!
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Before we start, let's confirm that the point is indeed on the line, as the statement suggests:
The point is on the line. Next we want to find the derivative of the function. We apply implicit differentiation and differentiate both sides:
The left hand side was obtained via the chain rule and the right hand side was obtained via a product rule.
Substitute in the given point.
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