Appendix B — Math

B.1 Differentiation

B.2 Integral

B.3 Partial derivative

A partial derivative measures how a function with multiple variables changes when you vary only one of those variables and keep the others fixed.

For example, to compute:

\[\frac{\partial(a^2 + b^2)}{\partial a}\]

• Treat \(b\) as if it were a constant.
• Since \(b^2\) is a constant with respect to \(a\), its derivative is 0.
• Take the derivative of \(a^2\) with respect to \(a\), which is \(2a\).

Hence:

\[\frac{\partial(a^2 + b^2)}{\partial a} = 2a\]