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 | v^{2} |
Basic formulas of derivatives
Derivatives of constant
c ′ = 0, где c = const
Derivatives of power functions
(x^{n} )′ = n · x^{n - 1}
Derivatives of exponential functions
(a^{x} )′ = a^{x} · ln a
Derivatives of exponential functions
(e^{x} )′ = e^{x}
Derivatives of logarithmic functions
Derivative of Trigonometric Functions
(sin x)′ = cos x
(cos x)′ = -sin x
Derivative of inverses trigonometric functions
(arcsin x)′ = | 1 | √1 - x^{2} |
(arccos x)′ = - | 1 | √1 - x^{2} |
(arcctg x)′ = - | 1 | 1 + x^{2} |
Derivative of Hyperbolic functions
(sh x)′ = ch x
(ch x)′ = sh x
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