Derivatives identities

Main derivatives identities can be obtained from the derivative definition by taking corresponding limits. Below represented all the rules needed to calculate the derivative of any expression.

Constant derivative:

c'=0, (c - constant)

Derivative of the sum is the sum of derivatives:

(u(x)+v(x))'= u(x)'+v(x)'

Derivative of the difference is the difference of derivatives:

(u(x)−v(x))'= u(x)'−v(x)'

Multiplication derivative:

(u(x)∙v(x))'=u(x)'∙v(x)+v(x)'∙u(x)

Fraction derivative:

Derivative of the composition of the functions:

F(u(x))'=F_u(x)^'(u(x))∙u(x)^'

Derivatives of some elementary functions:

Power function:

Root function:

Exponential and logarithmic functions:

Trigonometric functions:

sin(x)'=cos(x)

cos(x)'= −sin(x)

Exponential-power function:

Our online calculator maintains all the derivative rules, that is why it able to calculate the derivative of any, even very complicated function.