derivative

The Key Rules of Differentiation 1. Power rule (다항식의 미분에 핵심)If $f(x)=x^n$, where $n \in \mathbb{R}$, then the derivative of $f$ with respect to $x$ is $f^\prime(x)=nx^{n-1}$더보기https://youtu.be/m0xJM4AntQg?si=KjDW_SeYWwN-BZnF2. Constant ruleif $f(x)=c$ where $c \in \mathbb{R}$ and constant, then the derivative of $f$ with respect to $x$ is $f^\prime (x)=0$.3. Sum and Difference rule (미분의 선형성)$f$와..

Derivative (도함수) of Logistic Function (Sigmoid라고도 불림) $y=\sigma(x)=\dfrac{1}{1+e^{-x}}$ 를 미분하면 다음과 같음. $$\frac{d}{dx}\sigma(x)= \sigma(x)(1-\sigma(x))$$ graph 유도 유도는 다음과 같음. $$\begin{aligned}\frac{d}{dx}\sigma(x)&= \dfrac{0\times(1+e^{-1}) - 1\times(-e^{-1})}{(1+e^{-x})^2}\\&=\dfrac{e^{-x}}{(1+e^{-x})^2}\\ &= \frac{1}{(1+e^{-x})}\frac{e^{-x}}{(1+e^{-x})}\\ &= \frac{1}{(1+e^{-x})}\left( 1-\dfrac{..

Derivative 란?"Differential을 구한다(Differentiation, 미분하다)" 는 derivative(도함수)를 구하는 것을 가르킴. Derivative(도함수)는average rate of change (평균변화율)의 limit인instantaneous rate of change (=derivative value, differential coefficient)(순간변화율◀ linear approximation의 slope)임.$$\displaystyle \dfrac{dy}{dx}=y^\prime=\lim_{\Delta x \to 0}\dfrac{f(x+\Delta x)-f(x)}{\Delta x}=\lim_{\Delta x \to 0}\dfrac{\Delta f(x)}{\Delta..