Differentiation — Formula Sheet

If y = f(u) and u = g(x), then dy/dx = (dy/du) × (du/dx)

If y = f(x) and x = f⁻¹(y), then dx/dy = 1/(dy/dx)

When differentiating y = f(g(x)), use dy/dx = (dy/du) × (du/dx) where u = g(x).

When variables cannot be separated (like x² + y² = a²), differentiate both sides with respect to x, treating y as a function of x.

When both x and y are functions of a parameter t (like x = f(t), y = g(t)), use dy/dx = (dy/dt)/(dx/dt), provided dx/dt ≠ 0.