If $f(x)=(x-b)^2, \quad f^\prime(x)=2(x-b)$
$$f^\prime(x)=\lim_{h \rightarrow 0}{{f(x+h)-f(x)} \over h}$$
-$$=\lim_{h \rightarrow 0}
## Euler's number as a limit
$$\lim_{h \rightarrow 0} {{e^h-1} \over h}=1$$
+
+## Chain rule
+
+Leibniz notation:
+
+$${dy \over dx} = {dy \over du} \times {du \over dx}$$
+
+Function notation:
+
+$$(f\circ g)^\prime(x)=f^\prime(g(x))g^\prime(x),\quad \mathbb{where}\hspace{0.3em} (f\circ g)(x)=f(g(x))$$
+
+Used with only one expression.
+
+e.g. $y=(x^2+5)^7$ - Cannot reasonably expand
+Let $u-x^2+5$ (inner expression)
+${du \over dx} = 2x$
+$y=u^7$
+${dy \over du} = 7u^6$
+
+
+$7u^6 \times$
+