Know how and good skills in **functions derivatives** calculation is very important in science and engineering. On this website you can find plenty of examples about functions derivatives which are solved step by step. We often use functions derivatives to find maxium or minimum value of function. Good mathematical skills are very important.

We are lucky because we don't have to designate all derivatives of functions. Mathematicians had designated plenty of basic derivatives of functions. Most of functions which you will meet are complex of basic functions. Below are placed basic functions derivatives and some basic theorems about function derivatives.

Basic derivatives of functionsCalculation of function derivative which form is f(x)=2·x. Definition of derivative will be used to calculate derivative of this function.

Function derivative - example 1
Calculation of function derivative which form is f(x)=x^{2}. Definition of derivative will be used to calculate derivative of this function.

Calculation of function derivative which form is f(x)=3·x^{2}+4·x-1.

Calculation of function derivative which form is f(x)=(x-5)·e^{x}.

Calculation of function derivative which form is f(x)=cos(5·x)+e^{-2·x}.

Calculation of function derivative which form is f(x)=cos(5·x)·e^{-2·x}. Considered function is multiply of two complex functions.

Calculation of function derivative which form is f(x)=(3/(x+7))^{2}. Considered function is a complex functions.

Calculation of function derivative which form is f(x)=sin^{2}x. Considered function is a complex functions.

Calculation of function derivative which form is f(x)=2·x·e^{-x2}. Considered function is a multipy of complex function and non-complex function.

Derivative calculation of function f(x)=x^{1/2}+ln(x). Considered function is a sum of two component functions. First component function is a square root of variable x. Second component function is natural logarithm of variable x.

Derivative calculation of function f(x)=x^{1/2}·ln(x). Considered function is a multiply of two component functions. First component function is a square root of variable x. Second component function is natural logarithm of variable x. Theorem about derivative of two functions multiply will be applied.

Derivative calculation of function f(x)=x^{4}·e^{x}. Considered function is a multiply of two component functions. First component variable x taken to the fourth power. Second component function is constant e to the x power. Theorem about derivative of two functions multiply will be applied.

Derivative calculation of function f(x)=x/(x^{2}+1). Considered function is a divide of two component functions. First component variable x taken to the first power. Second component function is constant one plus variable x taken to the second power. Theorem about derivative of two functions multiply will be applied. Theorem about derivative of complex function will be applied.

Derivative calculation of function f(x)=x^{1/2}. Considered function is a square root of variable x. On the other hand this function may be written in form as variable x taken to the power of one-half.

Derivative calculation of function f(x)=(x^{1/2}+1)/(x^{1/3}). Considered function is a divide of two component functions. First component function is a constant one plus variable x in power one-half. Second function is variable x in power one-third.

Derivative calculation of function f(x)=(sin(x))/(x+1). Considered function is a divide of two component functions. First component function is function sin(x). Second function is variable x plus one.

Function derivative - example 16Derivative calculation of function f(x)=x/cos(x). Considered function is a divide of two component functions. First component function is variable x. Second function is cos(x). Theorems about derivative of two function multiply and derivative of complex function will be applied.

Function derivative - example 17
Derivative calculation of function f(x)=(1-x^{3})/(1+x^{3}). Considered function is a divide of two component functions. First component function is (1-x^{3}). Second component function is (1+x^{3}). Theorems about derivative of two function multiply and derivative of complex function will be applied.

Derivative calculation of function f(x)=x·sin^{2}x. Considered function is a multiply of two component functions. First component function is x. Second component function is sin^{2}x. Theorems about derivative of two function multiply and derivative of complex function will be applied.

Derivative calculation of function f(x)=x·(1+x^{2})^{1/2}. Considered function is a multiply of two component functions. First component function is x. Second component function is (1+x^{2})^{1/2}. Theorems about derivative of two function multiply and derivative of complex function will be applied.

Derivative calculation of function f(x)=e^{(1+x)/(1-x)}. Considered function is a complex function. Theorems about derivative of two function multiply and derivative of complex function will be applied.

Derivative calculation of function f(x)=x^{2}·e^{2·x}. Considered function is a multiply of two component functions. First component function is x^{2}. Second component function is e^{2·x}. Theorems about derivative of two function multiply and derivative of complex function will be applied.

Derivative calculation of function f(x)=(1+x^{2})^{1/2}·ln(x). Considered function is a multiply of two component functions. First component function is (1+x^{2})^{1/2}. Second component function is ln(x). Theorems about derivative of two function multiply and derivative of complex function will be applied

Derivative calculation of function f(x)=sin(ln(2·x)). Considered function is a complex function. Outside function is sin(). First inner function is ln(). second inner function is 2·x. Theorems about derivative of two function multiply and derivative of complex function will be applied.

Function derivative - example 24
Derivative calculation of function f(x)=sin^{2}(2·x). Considered function is a complex function. Outside function is sin^{2}(). Inner function is 2·x. Theorems about derivative of two function multiply and derivative of complex function will be applied.

Derivative calculation of function f(x)=(1+ln(x^{2}+1))^{1/2}. Considered function is a triple complex function. Outside function is power^{(1/2)}. First inner function is natural logarithm ln(). Second inner function is x^{2}+1. Theorems about derivative of complex function will be applied.

Derivative calculation of function f(x)=sinh(x)=(e^{x}-e^{-x})/2. It is know from formulas for derivatives of elementary functions that derivative of hiperbolic sine is a hiperbolic cosine. In example derivative of hiperbolic sine is calculated for its exponent form.

Derivative calculation of function f(x)=cosh(x)=(e^{x}+e^{-x})/2. It is know from formulas for derivatives of elementary functions that derivative of hiperbolic cosine is a hiperbolic sine. In example derivative of hiperbolic cosine is calculated for its exponent form.

Derivative calculation of function f(x)=5·x^{3}+2·x^{4}+sin(x). Considered function is a sum of three component function. Theorem about derivative for sum of three functions will be used.

Derivative calculation of function f(x)=(sin(x))^{3}+(cos(x))^{3}. Considered function is a sum of two component functions. Both component functions are complex functions. Theorems about derivative of sum of two functions and derivative of complex function will be used.

Derivative calculation of function f(x)=(sin(x))^{3}·(cos(x))^{3}. Considered function is a multiply of two component functions. Both component functions are complex functions. Theorems about derivative of multiply of two functions and derivative of complex function will be used.