IOAI ML Notes Mathematics FundamentalsCalculus

Derivatives and Partial Derivatives

Math fundamentals note for IOAI ML preparation.

16 February 2026

Syllabus Map

Study map: Syllabus Study Map

Core Idea

Derivative measures rate of change.
Partial derivative changes one variable at a time in multivariate functions.

Key Formulas

\frac{d}{dx}x^n = nx^{n-1}

\frac{\partial f}{\partial x_i}

Practical Notes

Derivative sign indicates direction of change.

Positive increases, negative decreases locally.

Magnitude indicates sensitivity.

Larger absolute values mean stronger local effect.

Why This Matters for ML

Parameter updates depend on partial derivatives of loss with respect to each weight.
Sensitivity analysis of features and parameters uses derivative magnitude and sign.
Regularizers and constraints are optimized through derivative-based updates.
Understanding local rate of change is necessary for debugging training dynamics.

← Back to Blog