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Differentiation Formulas
Differentiation Formulas
We found
29
formulas for differentiation
1.
$\dfrac{d}{dx}\, \left(C\right) = 0$
Differentiation
Variables:
C
→
Real number
2.
$\dfrac{d}{dx}\, \left(x\right) = 1$
Differentiation
3.
$\dfrac{d}{dx}\, \left(ax+b\right) = a$
Differentiation
Variables:
a, b
→
Real numbers
4.
$\dfrac{d}{dx}\, \left(ax^2+bx+c\right) = 2ax+b$
Differentiation
Variables:
a, b, c
→
Real numbers
5.
$\dfrac{d}{dx}\, \left( x^n \right) = nx^{n-1}$
Differentiation
Variables:
n
→
Integer
6.
$\dfrac{d}{dx}\, \left(x^{-n}\right) = -\dfrac{n}{x^{n+1}}$
Differentiation
Variables:
n
→
Integer
7.
$\dfrac{d}{dx}\, \left( \dfrac{1}{x} \right) = -\dfrac{1}{x^2}$
Differentiation
8.
$\dfrac{d}{dx}\, \left( \sqrt{x} \right) = \dfrac{1}{2\sqrt{x}}$
Differentiation
9.
$\dfrac{d}{dx}\, \left( \sqrt[n]x \right) = \dfrac{1}{n \sqrt[n]{x^{n-1}}}$
Differentiation
Variables:
n
→
Integer
10.
$\dfrac{d}{dx}\, \left( \ln x \right) = \dfrac{1}{x}$
Differentiation
11.
$\dfrac{d}{dx}\, \left( \log_ax \right) = \dfrac{1}{x\,\ln a}$
Differentiation
12.
$\dfrac{d}{dx}\, \left(e^x \right) = e^x$
Differentiation
13.
$\dfrac{d}{dx}\, \left( a^x \right) = a^x \ln a$
Differentiation
14.
$\dfrac{d}{dx}\, \left( \sin x \right) = \cos x$
Differentiation
15.
$\dfrac{d}{dx}\, \left( \cos x\right) = -\sin x$
Differentiation
16.
Derivative of tan x
$\dfrac{d}{dx}\, \left( \tan x \right) = \frac{1}{\cos^2 x}$
Differentiation
17.
Derivative of cotangent
$\dfrac{d}{dx}\, \left( \cot x\right) = -\dfrac{1}{\sin^2x}$
Differentiation
18.
Differentiation of arcsin x
$\dfrac{d}{dx}\, \left( \sin^{-1} x\right) = \dfrac{1}{\sqrt{1-x^2}}$
Differentiation
19.
Derivative od arccosx
$\dfrac{d}{dx}\, \left( \cos^{-1} x\right) = -\dfrac{1}{\sqrt{1-x^2}}$
Differentiation
20.
Derivative of arctanx
$\dfrac{d}{dx}\, \left( \tan^{-1} x\right) = \dfrac{1}{1+x^2}$
Differentiation
21.
Derivative of arccotx
$\dfrac{d}{dx}\, \left( \cot^{-1} x\right) = -\dfrac{1}{1+x^2}$
Differentiation
22.
Derivative od sinh x
$\dfrac{d}{dx}\, \left( \sinh x\right) = \cosh x$
Differentiation
23.
Derivative od cosh x
$\dfrac{d}{dx}\, \left( \cosh x\right) = \sinh x$
Differentiation
24.
Derivative od tanh
$\dfrac{d}{dx}\, \left( \tanh x\right) = \dfrac{1}{\cosh^2x}$
Differentiation
25.
Derivative od coth x
$\dfrac{d}{dx}\, \left( \coth x\right) = -\dfrac{1}{\sinh x}$
Differentiation
26.
Derivative of inverse sinh
$\dfrac{d}{dx}\, \left( \sinh^{-1} x\right) = \dfrac{1}{\sqrt{x^2+1}}$
Differentiation
27.
Derivative of inverse cosh
$\dfrac{d}{dx}\, \left( \cosh^{-1} x\right) = \dfrac{1}{\sqrt{x^2-1}}$
Differentiation
28.
Derivative od inverse tanh
$\dfrac{d}{dx}\, \left( \tanh^{-1} x\right) = \dfrac{1}{1-x^2}$
Differentiation
29.
Derivative of inverse coth
$\dfrac{d}{dx}\, \left( \coth^{-1} x\right) = \dfrac{1}{1-x^2}$
Differentiation
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Factoring formulas
Product formulas
Exponents formulas
Square roots formulas
Higher roots formulas
Logarithm
Set Identities
Complex Numbers
Logic
Equilateral triangle
Isoscales triangle
Right Triangle
Scalene Triangle
Rectangle
Square
Rhombus
Parallelogram
Cyclic Quadrilateral
Circle
Radians and Degrees
Most Important Formulas
Sum and difference formulas
Double angle formulas
Half-angle formulas
Multiple Angle Formulas
Sum to product
Product To Sum
Power of trigonometric functions
Two - dimensional coordinate system
Line in plane
Circle
Ellipse
Hyperbola
Limits of Functions
Differentiation rules
Differentiation Formulas
Derivatives of Composite Functions
Higher Order Derivatives
Integrals of Rational Functions
Integrals of Irrational Functions
Integrals of Trigonometric Functions
Integrals of exponential and logarithmic functions
Integrals of hyperbolic functions
Arithmetic series
Geometric series
Finite sums
Power series