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 · 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

(log_a 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

Factoring: Some special cases Formulas and properties of exponents Formulas and properties of nth root Formulas and properties of logarithms Formulas and properties of arithmetic sequence Formulas and properties of geometrical sequence Trigonometry formulas Derivative formulas Integrals table

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