Free module · Calculus & mathematical models

Differential Calculus: Limits & Derivatives

Understand change, then learn the rules for measuring it. No finance background is needed.

functions · limits · slopes · chain rule · optimisation

Lessons in this module

1. Start with a straight line: input, output and slope
2. Functions, limits and continuity
3. The derivative: from an average slope to an instantaneous rate
4. Core derivative rules: constants, powers and sums
5. Derivative rules: powers, products, quotients and compositions
6. Chain rule workshop: nested functions and backpropagation
7. Second derivatives, Taylor expansions and numerical error
8. Stationary points, optimisation and Newton’s method
9. Implicit and inverse differentiation: sensitivities of solved parameters
10. Logarithmic differentiation and elasticities
11. L’Hôpital’s rule: resolve indeterminate ratios carefully

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Practice and apply

• Build a tangent and check its error — For f(x)=x³ at x=2, estimate f(2.1) using first and second derivatives.
• Chain rule workshop: nested functions and backpropagation — Evaluate 6*256*6 in loss units per input unit.
• Implicit and inverse differentiation: sensitivities of solved parameters — Evaluate 1/(2*2) in parameter units per input unit.
• Logarithmic differentiation and elasticities — Evaluate 1*(0+1) in dimensionless elasticity.
• L’Hôpital’s rule: resolve indeterminate ratios carefully — Evaluate 1 in dimensionless limiting ratio.
• Evaluate a function — For f(x)=2x+1, calculate f(4).
• Constant slope — Find the derivative of f(x)=9.

Work through the practice exercises · Quant development tools