Proof: Euler's Equation Created: 10 January 2020 Last Updated: 10 January 2020 \[e^{ix}=\cos x + i\sin x\]

Why Integration Gives The Area (The Fundamental Theorem of Calculus)) Created: 05 January 2020 Last Updated: 05 January 2020

Proof: The Product and Quotient Rules Created: 04 January 2020 Last Updated: 04 January 2020 \[\frac{d}{dx}\left(\frac{u}{v}\right)=\frac{v \frac{du}{dx}-u \frac{dv}{dx}}{v^2}\] \[\frac{d}{dx}(uv)=u \frac{dv}{dx}+v \frac{du}{dx}\] where u and v are functions of x.

Proof: The Derivative of sin(x) in Radians Created: 02 January 2020 Last Updated: 20 January 2020 \(\frac{d}{dx} \sin x = \cos x\) when x is in radians

Proof: Binomial Expansion for Negative and Fractional n Formula Created: 02 January 2020 Last Updated: 02 January 2020

Fibonacci nth Term Formula Proof (Binet's Formula) Created: 01 January 2020 Last Updated: 02 January 2020

Addition Formulae Proof using Euler's Equation Created: 27 December 2019 Last Updated: 10 January 2020

Double Angle Formulae Proof using Euler's Equation Created: 27 December 2019 Last Updated: 10 January 2020

Variance and Standard Deviation Formula Proof Created: 27 December 2019 Last Updated: 28 December 2019

Differentiation by First Principles Formula Proof Created: 26 December 2019 Last Updated: 27 December 2019