+## Derivatives of $x^n$
+
+For $f: \mathbb{R} \rightarrow \mathbb{R}$ where $f(x)=x^n, x \in \mathbb{N}$
+
+Derivative is $f^\prime(x) = nx^{n-1}$
+
+If $x=$ constant, derivative is $0$
+
+If $f(x)={1 \over x}=x^{-1}, \quad f^\prime(x)=-1x^{-2}={-1 \over x^2}$
+
+If $f(x)=^5\sqrt{x}=x^{1 \over 5}, \quad f^\prime(x)={1 \over 5}x^{-4/5}={1 \over 5 \times ^5\sqrt{x^4}}$
+
+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}
+