# How do you find #(dy)/(dx)# given #x^2+y^2=1#?

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To find (dy)/(dx) given x^2+y^2=1, you can implicitly differentiate both sides of the equation with respect to x, and then solve for (dy)/(dx).

Differentiating both sides of the equation x^2 + y^2 = 1 with respect to x:

d/dx(x^2) + d/dx(y^2) = d/dx(1)

2x + 2y(dy/dx) = 0

Now, solve for (dy)/(dx):

2y(dy/dx) = -2x

(dy/dx) = (-2x) / (2y)

(dy/dx) = -x / y

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