Table Of Derivatives

Rules On Differentiation Product Rule: $$\frac{d}{dx} \left( uv \right) = v \frac{du}{dx} + u \frac{dv}{dx}$$ ,where u, v are functions of x Quotient Rule: $$\frac{d}{dx} \left(\frac{u}{v} \right) = \frac{v\frac{du}{dx} – u \frac{dv}{dx}}{v^{2}}$$ Chain Rule: $$\frac{d}{dx} \left[ f\left(u \right) \right] = \frac{d}{du} \left[ f \left( u \right) \right] \times \frac{du}{dx}$$ Integration By Parts: $$\int \! u \, \text{d}v = uv-\int \! …

Read more

Hyperbolic Functions

Useful Hyperbolic functions references: Hyperbolic Identities: $$\cosh^{2}{u}-\sinh^{2}{u} = 1$$ $$1-\text{tanh}^{2} u = \text{sech}^{2}u$$ $$\text{coth}^{2} u-1 = \text{cosech}^{2} u$$ $$\sinh{\left(x \pm y \right)} = \sinh{x}\cosh{y} \pm \cosh{x}\sinh{y}$$ $$\cosh{\left(x \pm y \right)} = \cosh{x}\cosh{y} \pm \sinh{x}\sinh{y}$$ $$\sinh{2u} = 2 \sinh{u}\cosh{u}$$ $$\begin{aligned} \cosh{2u} &= \cosh^{2}{u} + \sinh^{2}{u} \\ &= 2 \cosh^{2}{u}-1 \\ &= 1 + 2\sinh^{2}{u} \end{aligned}$$ Relation between inverse hyperbolic functions and …

Read more

Trigonometry

Some useful references on Trigonometry: Basic Trigonometric Identities: $$\begin{aligned}\sin^{2}{\theta} + \cos^{2} \theta &= 1 \\ 1 + \tan^{2} \theta &= \sec^{2} \theta \\ 1 + \cot^{2} \theta &= \csc^{2} \theta \end{aligned}$$ Compound Angle Relations: $$\begin{aligned} \sin{\left( A \pm B \right)} &= \sin{A}\cos{B} \pm \cos{A}\sin{B} \\ \cos{\left( A \pm B \right)} &= \cos{A}\cos{B} \mp \sin{A}\sin{B} \\ \tan{\left(A \pm B \right)} &= …

Read more

Dropbox – An online cloud storage service

Dropbox is a freemium cloud storage service which has an excellent desktop sync client. I have been using dropbox since 2011 and I am extremely satisfied with the service. I have mostly been using it as a cloud storage device, accessing my files on dropbox from my smartphone. Pros: – 2 GB free space which can be expanded by referring …

Read more

Learn how to google effectively

I came across this picture and thought it would be a nice addition to this blog. Being able to conduct online research effectively IS a valuable skill. It will help you to save A LOT of time and effort. Back To Interesting Things

7 Tips To Take Better Care Of Your Rechargeable Batteries

Do you have those rechargeable batteries? Do you want to know how to get the most out of them? Then, you have come to the right place! Note: If you are looking for information about the battery in your smartphone (lithium ion), please visit https://www.miniphysics.com/7-tips-to-longer-lasting-battery.html. I will tell you how to prolong the useful lifespan of your rechargeable batteries, specifically nickel …

Read more