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October 20, 2014

October 20, 2014

Posted by **George** on Wednesday, November 5, 2008 at 12:34pm.

Is the answer 20x+8y=0

- Calculus -
**drwls**, Wednesday, November 5, 2008 at 12:42pmNo; that is not the right answer.

Differentiate both sides of the equation with respect to x. Because y is a function of x, this is called "implicit differentiation". You get

20 x + 8 y dy/dx = 0

Solve that for dy/dx

dy/dx = -20x/8y = -(5/2)(y/x)

Note that you did not have to solve for y(x) first to obtain this result for dy/dx. That is why implicit differentiation is so convenient.

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