Differentiation from First Principles

Differentiation from first principles finds the derivative directly from its definition as a limit: $f'(x)=\lim_{h\to 0}\frac{f(x+h)-f(x)}{h}$. It calculates the gradient of a chord and lets the gap $h$ shrink to zero, showing where the shortcut rules of differentiation come from.

You meet Differentiation from First Principles in the Differentiation chapter of SPM Additional Mathematics. Knowing the term precisely matters in the exam: questions often hinge on reading a keyword correctly, and because SPM marking is analytic, using the right definition in your working helps secure method marks.

Our teachers make sure a student can not only recite what Differentiation from First Principles means but use it fluently in a full solution.

Because the SPM Add Math paper is bilingual (BM/EN), it helps to know this term in each language: Differentiation from First Principles (EN) · Pembezaan dari Prinsip Pertama (BM) · 用第一原理求导 (中文)

Other key terms from the Differentiation chapter you may want to check:

• Limit
• First Derivative
• Gradient Function
• Chain Rule
• Product Rule
• Quotient Rule