數學環境中的疊加

Question

我正在為數學入門課準備一個演示文稿，在某個時候我想展示一個在「對齊」環境中編寫的證明，我想一步一步地揭示它。但是，我還沒有找到一種方法來使用\overlay、\pause或等命令來做到這一點\uncover。

那麼，有什麼方法可以覆蓋「對齊」環境內的方程式或部分方程式嗎？或者我必須在不同的環境中分割方程，然後使用 \pause 或任何其他命令（這會更難看）？

下面我附上了 MWE，任何幫助將不勝感激。

\documentclass[usenames,dvipsnames]{beamer}

% To add a table of contents at the beginning of each section
\AtBeginSection[]
{
  \begin{frame}
    \frametitle{Table of Contents}
    \tableofcontents[currentsection]
  \end{frame}
}
\setbeamertemplate{section in toc}[sections numbered] % To enumerate the table of contents

%\usetheme{CambridgeUS}

\definecolor{Red}{RGB}{176,23,31}

%This sequence of packages controls the mathematical tools of latex
\usepackage{amsmath}
\usepackage{mathtools}
% \usepackage{mathrsfs}
\usepackage{amssymb}
\usepackage{amsfonts}
\usepackage{bm} % to make math symbols bold

% A more advanced package for images and figures
\usepackage{graphicx}

% These packages controls the graphs
\usepackage{tikz}
    \usetikzlibrary{arrows.meta}
    \usetikzlibrary{decorations.pathreplacing}
    \usetikzlibrary{fit, calc, matrix, positioning, arrows.meta, intersections, through, backgrounds, patterns}
\usepackage{pgfplots}
    \pgfplotsset{compat = newest}
    \usepgfplotslibrary{fillbetween}
    \pgfplotsset{overwrite option/.style args={#1 with #2}{#1=#2,#1/.code=}}
    \pgfplotsset{
        vasymptote/.style={before end axis/.append code={\draw[dashed,<->,-{Latex}] ({rel axis cs:0,0} -| {axis cs:#1,0}) -- ({rel axis cs:0,1} -| {axis cs:#1,0}); }},
        myaxis/.style={axis line style={<->, {Latex}-{Latex}}}
        }   % This fancy shit sets the arrows to both parts of the axis in the axis environment of pgfplot
    
% to import certain files
\usepackage{import}

%% Useful packages

\usepackage[makeroom]{cancel}
\usepackage{lipsum,graphicx,subcaption}
\usepackage{float}
\usepackage{xcolor}
\usepackage{fourier}
\usepackage{multicol}
    \setlength{\columnsep}{5pt}
\usepackage{hyperref}
    \hypersetup{
        colorlinks=true,
        linkcolor=DarkOrchid,
        filecolor=magenta,      
        urlcolor=blue,
    }

\begin{document}


\begin{frame}{DERIVATIVES}
    \framesubtitle{IMPLICIT DIFFERENTIATION}
    
    Assuming $y$ depends on $x$ and using implicit differentiation on the second term: \pause
    \begin{align*}qy^{q-1}\frac{d y}{d x}=px^{p-1} & 
        \Leftrightarrow \frac{d y}{d x} = \frac{px^{p-1}}{qy^{q-1}} & \text{Solving for }\frac{d y}{d x} \pause\\
        & \Leftrightarrow \frac{d y}{d x} = \frac{px^{p-1}}{q\left(x^{\frac{p}{q}}\right)^{q-1}} &
        \text{Substituting } y \\
        & \Leftrightarrow \frac{d y}{d x} = \frac{px^{p-1}}{qx^{p-\frac{p}{q}}} & \text{Multiplying exponents} \\
        & \Leftrightarrow \frac{d y}{d x} = \frac{p}{q} x^{p-1-p+\frac{p}{q}}\\
        & \Leftrightarrow \frac{d y}{d x} = \frac{p}{q} x^{\frac{p}{q}-1} = 
        nx^{n-1}
    \end{align*}
    
\end{frame}

\end{document}

Answer 1

看看以下建議是否適合您：

\documentclass[usenames,dvipsnames]{beamer}
\usepackage{fourier}
\usepackage{mathtools, amssymb, bm} 

\usepackage{pgfplots} % it load tikz too
\usetikzlibrary{arrows.meta, 
                backgrounds, 
                calc, 
                decorations.pathreplacing,
                intersections, 
                matrix, 
                positioning, patterns,
                through}
\usepgfplotslibrary{fillbetween}
\pgfplotsset{compat=1.17}


\begin{document}
\begin{frame}{DERIVATIVES}
\framesubtitle{IMPLICIT DIFFERENTIATION}

Assuming $y$ depends on $x$ and using implicit differentiation on the second term: 
\begin{align*}
    \uncover<2->{
qy^{q-1}\frac{d y}{d x}=px^{p-1} 
    & \Leftrightarrow \frac{d y}{d x} = \frac{px^{p-1}}{qy^{q-1}} 
            & \text{Solving for }\frac{d y}{d x}    \\ } 
    \uncover<3->{
    & \Leftrightarrow \frac{d y}{d x} =
        \frac{px^{p-1}}{q\left(x^{\frac{p}{q}}\right)^{q-1}}
            &   \text{Substituting } y              \\ }
    \uncover<4->{
    & \Leftrightarrow \frac{d y}{d x} 
        = \frac{px^{p-1}}{qx^{p-\frac{p}{q}}} 
            & \text{Multiplying exponents}          \\ }
    \uncover<5->{
    & \Leftrightarrow \frac{d y}{d x} 
        = \frac{p}{q} x^{p-1-p+\frac{p}{q}}         \\ }
    \uncover<6->{
    & \Leftrightarrow \frac{d y}{d x} 
        = \frac{p}{q} x^{\frac{p}{q}-1} = nx^{n-1}      }
\end{align*}
\end{frame}

\end{document}

筆記:

• beamer載入包xcolor並且hyperref，
• mathtools載入amsmath,
• amssymb載入amsfont,
• pgfplots載入tikz
• float沒有太大意義，因為beamer不支持浮動

所以這些包不需要再次載入。