SPM Form 4 Add Maths_Chapter 09 Differentiation

In this chapter, students should know how to apply differentiation to the given equation including second differentiation.

ie:
Given equation: y= mxⁿ +c

First differentiation: dy/dx = m(n)(x^n-1)

Second differentiation: d²y/dx²=m(n)(n-1)(x^n-2)

One thing that students should look out in this differentiation chapter is that.. There is a Product Rule and Quotient Rule that students should apply when differentiating equations that involve a product and quotient, ie. y = uv and y = u/v

Product Rule:  dy/dx = u dv/dx + v du/dx
Quotient Rule: dy/dx = [v du/dx - u dv/dx]/ (v²)

There is another section in differentiation involving the Rate of Change. Students should know that, when talking about Rate, it is about Time. Thus, Chain Rule is introduced here.

dx/dt = dx/dy x dy/dt ; where dx/dy = 1/ (dy/dx)

Approximate Small Change is the last section in this chapter, which the video below will teach 2 types of questions regarding this section.

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