도함수

[Math] The Key Rules of Differentiation

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 $f^\prime(x)=nx^{n-1}$. 2. Constant rule if $f(x)=c$ 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 $g$ 모두 $x$에 대해 differentiable function이라면, 다..

[Math] Derivative of Logistic Function

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{..