Higher Education · Numerical Methods
Numerical Differentiation
What is it
Numerical differentiation estimates a function's derivative using nearby function values rather than an algebraic formula, typically via finite difference approximations like (f(x+h) - f(x)) / h.
Why it matters
Numerical differentiation is essential when a function is only known from discrete measured data points (with no algebraic formula available), such as sensor readings or experimental results, where a true derivative can't be calculated symbolically.
Exam tip
Choosing a smaller step size h generally improves accuracy, but making it too small introduces floating-point rounding errors — this trade-off means there's often an optimal, not minimal, step size for a given calculation.
Related topics
Want help mastering Numerical Differentiation?
Tell us about the student's goals and confidence — we'll design a personalised plan.