Question

how do you get the answer in here using implicit differentiation?

x^2 + y^2 = r^2

Answer 1

I take it we want to find dy/dx? To use implicit differentiation, we take the derivative of each term as usual, keeping in mind that y is a function of x, so the chain rule makes the dy/dx term appear. Taking the derivative of both sides then gets
\[2x + 2y \frac{dy}{dx} = 0\]since r is a constant. Now we just have to solve for dy/dx:
\[ \frac{dy}{dx} = \frac{-x}{y}\]

Answer 2

so if there's a constant in the formula, it would be zero automatically then?

Answer 3

The derivative of a constant is still zero, yes.