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:

uxvxuxvxvxuxvx2

Derivative of the composition of the functions:

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

Derivatives of some elementary functions:

Power function:

xnnxn1
1x1x2

Root function:

x12x

Exponential and logarithmic functions:

axaxlna
exex
logax1xlna
lnx1x

Trigonometric functions:

sin(x)'=cos(x)
cos(x)'= sin(x)
tgx1cos2x
ctgx1sin2x

Exponential-power function:

xxxxlnx1
xuxxuxuxlnuxuxx

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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