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  • Mathematics
    Calculus: Derivatives
    • Vectors
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            • Calculus
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                    • Special Functions
                      Derivative

                      For a given differentiable function f, find its derivative f' and the second order derivative f''
                      If the function f is specified as a function of a single variable, then f' will be a derivative d with the respect to that variable.
                      If, however, function is specified to depend on on more then one variable (here every non-numeric literal that is not denoting a function will be conisdered as a variable),
                      then derivatives f' and f'' will be considered as partial derivatives ∂ with the respect to every variable occuring in the formula.

                      Important Note:
                      Please be very careful to write a multiplication symbol * when writing a term consisting of multiplication of two (or more) variables x*y or parameters a*b.
                      Terms xy or ab are instances of a single variable 'xy' or 'ab' whose label consists of two characters.
                      Please enter the function you want to differentiate:f=
                      First Order Derivative
                      Second Order Derivative
                      Syntax:
                      < formula >:=<number> |<variable> |<operation> |<function>; |(<formula>) |
                      <differential formula>
                      < equation >:=<formula>=<formula>
                      < differential equation >:=<equation>
                       
                      < operation >:=<unary operation> |<binary operation> |
                      < unary operation >:=-<formula> 
                      < binary operation >:=<formula><binary operator><formula>
                      < binary operator >:=+ |- |* |/ |^
                       
                      < differential formula >:=<formula>' |d(<formula>) |∂(<formula>) |
                       
                      < function >:=<functor>(<arguments>)
                      < arguments >:=<formula> |<formula>,<arguments>
                      < functor >:=See list of available functions bellow
                       
                      < number >:=<unsigned number> |-<unsigned number>
                      < unsigned number >:=<digits> | <digits>.<digits> | <special number>
                      < digits >:=<digit> | <digit><digits>
                      < digit >:=0 | 1 |2 |3 |4 |5 |6 |7 |8 |9
                      < special number >:=pi | e
                       
                      < variable >:=<letter> | <letter><alphanumerics>
                      < alphanumerics >:=<alphanumeric> | <alphanumeric><alphanumerics>
                      < alphanumeric >:=<letter> | <digit>
                      < letter >:=a | ... | z | A | ... | Z
                      Available Functions:
                      NameDescription# of
                      arguments
                      Trigonometric
                      sinsine function of an angle1
                      coscosine function of an angle1
                      tantangent function of an angle1
                      cotcotangent function of an angle1
                      secsecant function of an angle1
                      csccosecant function of an angle1
                      Inverse Trigonometric
                      arcsininverse of sine function1
                      arccosinverse of cosine function1
                      arctaninverse of tangent function1
                      arccotinverse of cotangent function1
                      arcsecinverse of secant function1
                      arccscinverse of cosecant function1
                      Logaritmic
                      lnnatural logarithm to the base e1
                      log10logarithm to the base 102
                      loglogarithm, with 1st argument as a base, of the 2nd argument2
                      Power and Root
                      sqrtsquare root1
                      rootfirst argument root of the second argument2
                      Miscellaneous
                      absabsolute value1
                      sgnsign or signum function1
                      Please Note:
                      • Multiplication must be explicitely specified with the "*" operator as "a*x" and not as "a x".
                      • Function arguments must be enclosed within parenthesis "( ... )", like "sin( x )" and not like "sin x".
                        There can't be a space between the functor and the open parenthesis for the arguments.
                      • Character sequences pi and e are treated as special numbers and not as variables.
                      • Equations, including differential must be specified as proper equations with "=" character.
                      • If you need to use an indexed variable, like xi (for example x1, x2,...) , please use the the index numbers as suffixes to the variable names, like x1, x2, ...
                      Examples:
                      tan(x)tan(x) = sin(x)cos(x)
                      log(a,b)loga(b)
                      ln(e^x)ln ( e x ) = x
                      abs(-2)| -2 | = 2
                      cos(pi/3)cos(π3) = 12
                      root(x, y)
                      x
                      √
                      y
                      y'=2*x*yy' = 2xy