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| Math Central | Quandaries & Queries |
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Question from Emily, a student: determine the derivative y' at the point (1,0) y'(1)= ?? |
Hi Emily.
When you implicitly differentiate with respect to x, you get y' on the left side obviously. You need to use the chain rule to differentiate the right side. [ln(x)]' = 1/x, so [ln(x2 + y2]] ' = [x2 + y2]' / (x2 + y2) and so on. Eventually you complete the chain rule and have an equation involving y', x and y.
Simply substitute at this point: x = 1, y = 0. Solve for y'.
Hope this helps,
Stephen La Rocque.
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