Implicit Differentiation Guide
Differentiate classic implicit curves step by step — then get dy/dx and the tangent line at your point.
The point should lie on the curve (the tool checks). Default: (3, 4) on x² + y² = 25.
① Answer
② Steps
③ Why it works
When y is tangled inside an equation, you cannot solve for y first — so you differentiate every term with respect to x and let the chain rule handle y: d/dx[yⁿ] = n·yⁿ⁻¹·dy/dx. The product rule handles mixed terms like xy. Then you collect every dy/dx term on one side and solve, exactly like solving a linear equation for an unknown.