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# Derivative formulas

Calculation of the derivative — the most important operation in differential calculus.

## Functions differentiation formula

In the table below u and v — are functions of the variable x, and c — is constant. It is enough these formulas to differentiate any elementary function.
(c · u)′ = c · u
(u + v)′ = u ′ + v
(u · v)′ = u ′ · v + u · v
 ( u ) ′ = u ′ · v - u · v ′ v v2

## Basic formulas of derivatives

### Derivatives of constant

c ′ = 0, где c = const

### Derivatives of power functions

(xn )′ = n · xn - 1

### Derivatives of exponential functions

(ax )′ = ax · ln a

(ex )′ = ex

### Derivatives of logarithmic functions

 (loga x)′ = 1 x · ln a
 (ln x)′ = 1 x

### Derivative of Trigonometric Functions

(sin x)′ = cos x
(cos x)′ = -sin x
 (tg x)′ = 1 cos 2 x
 (ctg x)′ = - 1 sin 2 x

### Derivative of inverses trigonometric functions

 (arcsin x)′ = 1 √1 - x2
 (arccos x)′ = - 1 √1 - x2
 (arctg x)′ = 1 1 + x2
 (arcctg x)′ = - 1 1 + x2

### Derivative of Hyperbolic functions

(sh x)′ = ch x
(ch x)′ = sh x
 (th x)′ = 1 ch2 x
 (cth x)′ = - 1 sh2 x