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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
vv2

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

Derivatives of exponential functions

(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

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