Differentiation and its Applications — Formula Sheet

Use chain rule

d/dx(y²) = 2y·dy/dx

dy/dx = (dy/dt)/(dx/dt), provided dx/dt ≠ 0

Second derivative

d²y/dx² = d/dx(dy/dx)

Third derivative

d³y/dx³ = d/dx(d²y/dx²)

Higher order derivatives

d^n y/dx^n = f^(n)(x)

When both x and y are expressed in terms of a parameter t, we use dy/dx = (dy/dt)/(dx/dt).

Revenue function R(x) = price × quantity.