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: $$\int \! u \, \text{d}v = uv-\int \! …
Useful Hyperbolic functions references: Hyperbolic Identities: $$\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}$$ Relation between inverse hyperbolic functions and …
Some useful references on Trigonometry: Basic Trigonometric Identities: $$\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)} &= …
References: Trigonometry Hyperbolic Functions Taylor Series Differentiation – Table Of Derivatives Integration – Integration Table Vectors Vector Analysis