Differentiation
Differentiation Rules







Note:

Chain Rule
For
and
,




Further Differentiation Rules (Chain Rule)






Product Rule

Quotient Rule

Gradient Of Curve
From
,
is the gradient of the curve.


Gradient Of Tangent & Normal
From
, substitute
to get
(gradient of tangent).
is the gradient of the normal.




Increasing & Decreasing Functions
1. For increasing functions,
\dfrac{\text{d}y}{\text{d}x}<0
\dfrac{\text{d}y}{\text{d}t}=\dfrac{\text{d}y}{\text{d}x}\times\dfrac{\text{d}x}{\text{d}t}
\dfrac{\text{d}y}{\text{d}x}=0
x=k
k^-
k
k^+

![Rendered by QuickLaTeX.com .[/stextbox] [stextbox caption="Rates Of Change" stextbox id="info"]](https://teach.sg/wp-content/ql-cache/quicklatex.com-d6569e51e60b9302b073cb6a581e8ede_l3.png)
![Rendered by QuickLaTeX.com [/stextbox] [stextbox caption="First Derivative Test" stextbox id="default"]If](https://teach.sg/wp-content/ql-cache/quicklatex.com-db52040a4d707e532107dfe5b3a967db_l3.png)




\dfrac{\text{d}^2y}{\text{d}x^2}<0\$, it is a maximum point.
2. If , it is a minimum point.
3. If , need to do first derivative test.