Differentiation Techniques Pt.2

A function can be written as athe product of two other functions. The product rule states that if you let \(F(x) = f(x) \cdot g(x)\), then \[F^{\prime}(x) = \frac{d}{dx}[f(x) \cdot g(x)] = f(x) \cdot \Bigg[ \frac{d}{dx}g(x) \Bigg] + g(x) \cdot \Bigg[ \frac{d}{dx}f(x) \Bigg]\] In simple English, the derivative of a product is the first factor times the derivative of the second factor, plus the second factor times the derivative of the first factor. …

Posted on

Differentiation Techniques

Let \(y\) be a function of \(x\). A common way to express “the derivate of \(y\) with respect to \(x\)” is the notation \[\frac{dy}{dy}\] Using this notation, we can write that if \(y = f(x)\), then the derivative of \(y\) with respect to \(x\) is \(\frac{dy}{dx} = f^{\prime}(x)\). There are a handful of rules that you can use when evaluating derivatives. The Power Rule states that \[\frac{d}{dx}x^k = kx^{k - 1}\] …

Posted on

Trading Technical Analysis - A Refreshing Take

There’s some controversy on whether technical analysis and chart reading are better than fundamental analysis and intrinsic valuation. I personally don’t have a dog in the fight. However, scanning reddit, I found a couple of interesting answers to a thread called “Change my mind: Technical Analysis is a complete nonsense” on r/CryptoCurrency Card And the original post on r/Bitcoin Card

Posted on

Differentiation Using Limits of Difference Quotients

A tangent line touches a curve at a single point only. For a function \(y = f(x)\), its derivative at \(x\) is the function \(f^{\prime}\) defined by \[f^{\prime}(x) = \lim_{h \to 0} \frac{f(x + h) - f(x)}{h}\] provided that the limit exists. If \(f^{\prime}(x)\) exists, then we say that \(f\) is differentiable at \(x\). The key concept here is that we’re taking the difference quotient between any two points of a function and reducing that difference \(f(x + h) - f(x)\) until it approaches \(0\). …

Posted on

Average Rates of Change

The average rate of change of \(y\) wih respect to \(x\), as \(x\) changes from \(x_1\) to \(x_2\), is the ratio of the change in output to the change in input: \[A(x) = \frac{f(x_2) - f(x_1)}{x_2 - x_1}\] where \(x_2 \neq x_1\). The average rate of change is the secant line passing through two points. If we generalize this idea we arrive at the different quotient, an average rate of change over any interval of a function. …

Posted on