Differentiation Rules

Today, we will recap the four basic rules of Differentiation:

  • Differentiating Powers of x

\displaystyle\frac{d}{dx}x^n=nx^{n-1}

(Power comes down, and the remaining power reduced by 1)

  • Chain Rule (i.e. times differentiate inside the bracket)
  • Product Rule

\displaystyle\frac{d}{dx}(uv)=u\frac{dv}{dx}+v\frac{du}{dx}

(Keep the first term X differentiate the second, PLUS keep the second term X differentiate the first)

  • Quotient Rule

\displaystyle\frac{d}{dx}(\frac{u}{v})=\frac{v\frac{du}{dx}-u\frac{dv}{dx}}{v^2}

(Keep the bottom term differentiate the top MINUS keep the top differentiate the bottom, whole thing over v^2)

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COE Quota: Math Formula

Applications of Math in Real Life: COE Quota

Source: http://en.wikipedia.org/wiki/Certificate_of_Entitlement

The Formula for COE Quota is:

\begin{align} (\text{Total COE Quota})_{qy} = &g.(\text{Motor vehicle population})_{y-1}  \\ &+ (\text{Projected de-registrations})_{y} \\&+ (\text{Unallocated quota})_{qy-1} \end{align}

Quote: In the formula above, the subscript y denotes calendar year and the subscript qy denotes quota year (May to April). Initially, projected deregistrations for (calendar) year y were simply taken to be equal to actual deregistrations in y-1 but from quota year 1999-2000 onwards, a projected number of deregistrations has been used.

Each year, the quota is set to allow for a targeted g percent growth in the total motor vehicle population, plus additional quota licenses to cover the number of motor vehicles that will be deregistered during the (calendar) year, plus any unallocated quota licenses from the previous quota year.

Read more at: http://en.wikipedia.org/wiki/Certificate_of_Entitlement

Online Base Converter Program for all bases

The Base Converter: Convert Base to any Base Program

Using this online javascript program (written by me a long time ago), we can convert a number to any base we desire.

Hope you have fun playing with this app!

For instance, let choose the number 88, and see what it is in different bases

In base 2: 1011000

Base 3: 10021

Base 4: 1120

Base 5: 323

Base 6: 224

Base 7: 154

Base 8: 130

Base 9: 107

Base 10: 88

Base 11: 80

Base 12: 74

Base 13: 6A

Base 14: 64

Base 15: 5D

Base 16: 58

Also, Learn how to convert bases manually