# Derivatives identities

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Main derivatives identities can be obtained from the derivative definition by taken 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:

### Exponential-power function:

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