1.
$\dfrac{d}{dx}\, \left(C\right) = 0$
2.
$\dfrac{d}{dx}\, \left(x\right) = 1$
3.
$\dfrac{d}{dx}\, \left(ax+b\right) = a$
4.
$\dfrac{d}{dx}\, \left(ax^2+bx+c\right) = 2ax+b$
5.
$\dfrac{d}{dx}\, \left( x^n \right) = nx^{n-1}$
6.
$\dfrac{d}{dx}\, \left(x^{-n}\right) = -\dfrac{n}{x^{n+1}}$
7.
$\dfrac{d}{dx}\, \left( \dfrac{1}{x} \right) = -\dfrac{1}{x^2}$
8.
$\dfrac{d}{dx}\, \left( \sqrt{x} \right) = \dfrac{1}{2\sqrt{x}}$
9.
$\dfrac{d}{dx}\, \left( \sqrt[n]x \right) = \dfrac{1}{n \sqrt[n]{x^{n-1}}}$
10.
$\dfrac{d}{dx}\, \left( \ln x \right) = \dfrac{1}{x}$
11.
$\dfrac{d}{dx}\, \left( \log_ax \right) = \dfrac{1}{x\,\ln a}$
12.
$\dfrac{d}{dx}\, \left(e^x \right) = e^x$
13.
$\dfrac{d}{dx}\, \left( a^x \right) = a^x \ln a$
14.
$\dfrac{d}{dx}\, \left( \sin x \right) = \cos x$
15.
$\dfrac{d}{dx}\, \left( \cos x\right) = -\sin x$
16.
Derivative of tan x
$\dfrac{d}{dx}\, \left( \tan x \right) = \frac{1}{\cos^2 x}$
17.
Derivative of cotangent
$\dfrac{d}{dx}\, \left( \cot x\right) = -\dfrac{1}{\sin^2x}$
18.
Differentiation of arcsin x
$\dfrac{d}{dx}\, \left( \sin^{-1} x\right) = \dfrac{1}{\sqrt{1-x^2}}$
19.
Derivative od arccosx
$\dfrac{d}{dx}\, \left( \cos^{-1} x\right) = -\dfrac{1}{\sqrt{1-x^2}}$
20.
Derivative of arctanx
$\dfrac{d}{dx}\, \left( \tan^{-1} x\right) = \dfrac{1}{1+x^2}$
21.
Derivative of arccotx
$\dfrac{d}{dx}\, \left( \cot^{-1} x\right) = -\dfrac{1}{1+x^2}$
22.
Derivative od sinh x
$\dfrac{d}{dx}\, \left( \sinh x\right) = \cosh x$
23.
Derivative od cosh x
$\dfrac{d}{dx}\, \left( \cosh x\right) = \sinh x$
24.
Derivative od tanh
$\dfrac{d}{dx}\, \left( \tanh x\right) = \dfrac{1}{\cosh^2x}$
25.
Derivative od coth x
$\dfrac{d}{dx}\, \left( \coth x\right) = -\dfrac{1}{\sinh x}$
26.
Derivative of inverse sinh
$\dfrac{d}{dx}\, \left( \sinh^{-1} x\right) = \dfrac{1}{\sqrt{x^2+1}}$
27.
Derivative of inverse cosh
$\dfrac{d}{dx}\, \left( \cosh^{-1} x\right) = \dfrac{1}{\sqrt{x^2-1}}$
28.
Derivative od inverse tanh
$\dfrac{d}{dx}\, \left( \tanh^{-1} x\right) = \dfrac{1}{1-x^2}$
29.
Derivative of inverse coth
$\dfrac{d}{dx}\, \left( \coth^{-1} x\right) = \dfrac{1}{1-x^2}$