\documentclass[12pt, a4paper]{article}
\title{Θㄧ计}
\author{﹎ ㏄ 89013900}

\begin{document}
\maketitle
ㄧ计 $f(x)$ 籔 $g(x)$ Θㄧ计 $f(g(x))$ 碞琌盢 $g(x)$  $f(x)$ ぇ跑计 $x$ 種
ㄒ $f(x) = x^2 + 1$$g(x) = \frac{1}{x}$玥
$$
f(g(x)) = g(x)^2 + 1 = \frac{1}{x^2} + 1 = f(\frac{1}{x})
$$
τΘ抖は筁ㄓ碞Θ
$$
g(f(x)) = \frac{1}{f(x)} = \frac{1}{x^2+1} = g(x^2 + 1)
$$

Θㄧ计旧ㄧ计そΑ嘿稬だ渺 $y = g(x)$$z = f(g(x))$玥
$$
\frac{d}{dx}f(g(x)) = \frac{dz}{dx} = \frac{dz}{dy}\frac{dy}{dx} = \frac{d}{dy}f(y)\cdot\frac{d}{dx}g(x)
$$
ㄒ $f$ 籔 $g$  $y = f(x)$玥
$$
\frac{d}{dx}\frac{1}{x^2 + 1} = \frac{d}{dx}g(f(x)) = \frac{d}{dy}g(y)\cdot\frac{d}{dx}f(x) = (-\frac{1}{y^2})(2x) = -\frac{2x}{(x^2 + 1)^2}
$$
\end{document}