基礎函式的微分運演算法則
冪函式法則$$\begin{align} \frac{d}{dx} x^n = nx^{n-1} \end{align}$$
指數函式法則$$\begin{align} \frac{d}{dx} e^x = e^x \end{align}$$$$\begin{align} \frac{d}{dx} a^x = ln(a)a^x \end{align}$$
對數函式法則$$\begin{align} \frac{d}{dx} ln(x) = \frac{1}{x} \end{align}$$$$\begin{align} \frac{d}{dx} log_a(x) = \frac{1}{xln(a)} \end{align}$$
三角函式法則$$\begin{align} \frac{d}{dx} sin(x) = cos(x) \end{align}$$$$\begin{align} \frac{d}{dx} cos(x) = -sin(x) \end{align}$$$$\begin{align} \frac{d}{dx} tan(x) = sin^2(x) = \frac{1}{cos^2(x)} = 1 + tan^2(x) \end{align}$$
反三角函式法則$$\begin{align} \frac{d}{dx} arcsin(x) = \frac{1}{\sqrt{1-x^2}}, -1 < x < 1 \end{align}$$$$\begin{align} \frac{d}{dx} arccos(x) = -\frac{1}{\sqrt{1-x^2}}, -1 < x < 1 \end{align}$$$$\begin{align} \frac{d}{dx} arctan(x) = \frac{1}{1+x^2} \end{align}$$
基礎函式的微分運演算法則
冪函式法則$$\begin{align} \frac{d}{dx} x^n = nx^{n-1} \end{align}$$
指數函式法則$$\begin{align} \frac{d}{dx} e^x = e^x \end{align}$$$$\begin{align} \frac{d}{dx} a^x = ln(a)a^x \end{align}$$
對數函式法則$$\begin{align} \frac{d}{dx} ln(x) = \frac{1}{x} \end{align}$$$$\begin{align} \frac{d}{dx} log_a(x) = \frac{1}{xln(a)} \end{align}$$
三角函式法則$$\begin{align} \frac{d}{dx} sin(x) = cos(x) \end{align}$$$$\begin{align} \frac{d}{dx} cos(x) = -sin(x) \end{align}$$$$\begin{align} \frac{d}{dx} tan(x) = sin^2(x) = \frac{1}{cos^2(x)} = 1 + tan^2(x) \end{align}$$
反三角函式法則$$\begin{align} \frac{d}{dx} arcsin(x) = \frac{1}{\sqrt{1-x^2}}, -1 < x < 1 \end{align}$$$$\begin{align} \frac{d}{dx} arccos(x) = -\frac{1}{\sqrt{1-x^2}}, -1 < x < 1 \end{align}$$$$\begin{align} \frac{d}{dx} arctan(x) = \frac{1}{1+x^2} \end{align}$$