Second derivative rule for parametric descriptions

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This article is about a differentiation rule, i.e., a rule for differentiating a function expressed in terms of other functions whose derivatives are known.
View other differentiation rules

Statement

Consider a parametric description of the form x = f(t), y = g(t), where f and g are functions of one variable. The second derivative rule states that:

\frac{d^2y}{dx^2} = \frac{f'(t)g''(t) - g'(t)f''(t)}{(f'(t))^3}

Facts used

  1. Definition of parametric derivative
  2. Quotient rule for differentiation