Given that $x^2 + y^2 = 25$, find $\dfrac{dy}{dx}$ at the point $(3, 4)$.

Differentiating implicitly: $2x + 2y\dfrac{dy}{dx} = 0$, so $\dfrac{dy}{dx} = -\dfrac{x}{y}$. At $(3, 4)$ this is $-\dfrac{3}{4}$. Inverting to $-\dfrac{y}{x}$ gives $-\dfrac{4}{3}$, and dropping the sign gives $\dfrac{3}{4}$.