Math CentralQuandaries & Queries


Question from Emily, a student:

determine the derivative y' at the point (1,0)
y= ln(x^2+y^2)

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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