在 (La)TeX 中添加限制

Question

我正在尝试添加多个限制。不是通过多个

\begin{atmProof}
\[F'(x)\] = \[\lim_{h\to0} \frac{F(x + h) - F(x)} {h}\] 
= $$\lim_{h\to0} \frac{f(x+h)g(x+h) - f(x)g(x)} {h}$$
\\
Now we subtract and add $f(x+h)g(x)$ :
\\
= $$\lim_{h\to0} \frac{f(x+h)g(x+h) -f(x+h)g(x) + f(x+h)g(x) - f(x)g(x)} {h}$$
\\
Now we can split the limit into two individual limits and factor each of them: 
\\
= $$\lim_{h\to0} \frac{f(x+h)[g(x+h) -g(x)]}{h}$$ +  $$\lim_{h\to0} \frac{g(x)         
[f(x+h) - f(x)]}{h}$$
\\
Substitute h for 0 into parts of the equation:

= $f(x)$ * $$\lim_{h\to0} \frac{g(x+h) -g(x)}{h}$$ +  $g(x)$ * $$\lim_{h\to0}      
\frac{f(x+h) - f(x)}{h}$$
\\
Therefore, by limit definition of the derivate:
\\
$F'(x) = f(x)g'(x) + g(x)f'(x)$

\end{atmProof}

我想要将两个限制添加在同一行。我该怎么做？

Answer 1

这也许是你想要的吗？（请注意，使用单个align*环境以及多个\intertext指令。align*环境和\intertext宏由​​包提供amsmath。）

\documentclass[a4paper,12pt]{article}
\usepackage{amsmath}
\allowdisplaybreaks % allow page breaks in lengthy "align" environments

\begin{document}
By definition, 
\begin{align*}
F'(x) 
&= \lim_{h\to0} \frac{F(x + h) - F(x)} {h}\\ 
&= \lim_{h\to0} \frac{f(x+h)g(x+h) - f(x)g(x)} {h}
\intertext{Now we subtract and add $f(x+h)g(x)$:}
&= \lim_{h\to0} \frac{f(x+h)g(x+h) -f(x+h)g(x) + f(x+h)g(x) - f(x)g(x)} {h}\\
\intertext{Now we can split the limit into two individual limits and factor each of them:}
&= \lim_{h\to0} \frac{f(x+h)[g(x+h) -g(x)]}{h} +  \lim_{h\to0} \frac{g(x)[f(x+h) - f(x)]}{h}\\
\intertext{Substitute $h$ for $0$ into parts of the equation:}
&= f(x) \times \lim_{h\to0} \frac{g(x+h) -g(x)}{h} +  g(x) \times \lim_{h\to0}\frac{f(x+h) - f(x)}{h}\\
\intertext{Therefore, by the limit definition of the derivate:}
F'(x) &= f(x)g'(x) + g(x)f'(x)\,.
\end{align*}

\end{document}