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:

fraction derivative

Derivative of the composition of the functions:

F(u(x))'=Fu(x)'(u(x))u(x)'

Derivatives of some elementary functions:

Power function:

derivative of the power function
derivative of the power function

Root function:

derivative of the root function

Exponential and logarithmic functions:

derivative of the exponential function
derivative of the exponential function
derivative of the logarithmic function
derivative of the logarithmic function

Trigonometric functions:

sin(x)'=cos(x)
cos(x)'= sin(x)
derivative of the tangent
derivative of the cotangent

Exponential-power function:

derivative of the exponential-power function
derivative of the 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.

Other useful links:

Parametric derivative online calculator
Derivative step by step sample

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