Practice Implicit Differentiation in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
A technique for finding \frac{dy}{dx} when y is defined implicitly by an equation F(x, y) = 0 rather than explicitly as y = f(x). Differentiate both sides with respect to x, treating y as a function of x, then solve for \frac{dy}{dx}.
Sometimes you can't (or don't want to) solve for y explicitly. Instead, differentiate the whole equation as-is. Every time you differentiate a y-term, attach \frac{dy}{dx} by the chain rule (since y secretly depends on x), then solve for \frac{dy}{dx}.
Example 1
easyFind \frac{dy}{dx} for the circle x^2 + y^2 = 25 and evaluate it at the point (3, 4).
Example 2
hardFind \frac{dy}{dx} for x^3 + y^3 = 6xy (folium of Descartes).
Example 3
easyFind \frac{dy}{dx} for x^2 + 3y^2 = 7.
Example 4
mediumFind the equation of the tangent line to x^2y + y^3 = 2 at the point (1, 1).