posted by George .
Find dy/dx of the function 10x^2+4y^2=sqrt(7).
Is the answer 20x+8y=0
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.