# Differentiation

Differentiation Rules

Note:
Chain Rule
For and ,

Further Differentiation Rules (Chain Rule)

Product Rule
Quotient Rule
From ,
is the gradient of the curve.
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}=0x=kk^-kk^+

\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.

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