2$(x^\alpha)'$
$\alpha x^{\alpha-1}$
3$\left(\frac{1}{x}\right)'$
$-\frac{1}{x^2}$
4$\left(\sqrt{x}\right)'$
$\frac{1}{2\sqrt{x}}$
5$(e^{\alpha x})'$
$\alpha e^{\alpha x}$
9$(tan(x))'$
$\frac{1}{cos^2(x)} = 1 + tan^2(x)$
10$(arccos(x))'$
$-\frac{1}{\sqrt{1 - x^2}}$
11$(arcsin(x))'$
$\frac{1}{\sqrt{1 - x^2}}$
12$(arctan(x))'$
$\frac{1}{1 + x^2}$
15$(th(x))'$
$\frac{1}{ch^2(x)} = 1 - th^2(x)$
16$((v \circ u)(x))'$
$u'(x) \times v'(u(x))$
17$(u(ax + b))'$
$a \times u'(ax + b)$
18$(u^\alpha(x))'$
$\alpha \times u'(x) \times u^{\alpha - 1}(x)$
19$\left(\frac{1}{u(x)}\right)'$
$-\frac{u'(x)}{u^2(x)}$
20$\left(\frac{u(x)}{v(x)}\right)'$
$\frac{u'(x)v(x) - v'(x)u(x) }{v^2(x)}$
21$(u(x) \times v(x))'$
$u'(x)v(x) + v'(x)u(x)$
22$\left(\sqrt{u(x)}\right)'$
$\frac{u'(x)}{2\sqrt{u(x)}}$
23$(e^{u(x)})'$
$u'(x)e^{u(x)}$
24$ln(u(x))$
$\frac{u'(x)}{u(x)}$