Posted by George on Wednesday, November 5, 2008 at 12:34pm.
Find dy/dx of the function 10x^2+4y^2=sqrt(7).
Is the answer 20x+8y=0

Calculus  drwls, Wednesday, November 5, 2008 at 12:42pm
No; 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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