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.