## The Mystery of the Sine of Nines, and a Math Olympiad question whose answer is 2015

Here are some of the latest updates back on http://mathtuition88.blogspot.com.

These two are highly recommended to view: The Mystery of the Sine of Nines, and a Math Olympiad question whose answer is 2015.

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## 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 $v^2$)