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z=arctg*(ln*(x^2+x-3))/x
Derivada de la función/ x^2+x/ arctg/ z=arctg*(ln*(x^2+x-3))/x

Derivada de z=arctg*(ln*(x^2+x-3))/x

Función f() - derivada -er orden en el punto
v

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
    /   / 2        \\
atan\log\x  + x - 3//
---------------------
          x
atan⁡(log⁡((x2+x)−3))x\frac{\operatorname{atan}{\left(\log{\left(\left(x^{2} + x\right) - 3 \right)} \right)}}{x} 
atan(log(x^2 + x - 3))/x
Gráfica
02468-8-6-4-2-1010-1010
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Trazar el gráfico f'(x)
Primera derivada [src] 
      /   / 2        \\                                        
  atan\log\x  + x - 3//                  1 + 2*x               
- --------------------- + -------------------------------------
             2              /       2/ 2        \\ / 2        \
            x             x*\1 + log \x  + x - 3//*\x  + x - 3/
2x+1x((x2+x)−3)(log⁡((x2+x)−3)2+1)−atan⁡(log⁡((x2+x)−3))x2\frac{2 x + 1}{x \left(\left(x^{2} + x\right) - 3\right) \left(\log{\left(\left(x^{2} + x\right) - 3 \right)}^{2} + 1\right)} - \frac{\operatorname{atan}{\left(\log{\left(\left(x^{2} + x\right) - 3 \right)} \right)}}{x^{2}}
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Segunda derivada [src] 
                                          2                  2    /          2\                                              
                                 (1 + 2*x)        2*(1 + 2*x) *log\-3 + x + x /                                              
                           -2 + ----------- + -------------------------------------                                          
      /   /          2\\                  2   /       2/          2\\ /          2\                                          
2*atan\log\-3 + x + x //        -3 + x + x    \1 + log \-3 + x + x //*\-3 + x + x /                 2*(1 + 2*x)              
------------------------ - -------------------------------------------------------- - ---------------------------------------
            2                       /       2/          2\\ /          2\               /       2/          2\\ /          2\
           x                        \1 + log \-3 + x + x //*\-3 + x + x /             x*\1 + log \-3 + x + x //*\-3 + x + x /
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                                                              x
−(2x+1)2x2+x−3+2(2x+1)2log⁡(x2+x−3)(log⁡(x2+x−3)2+1)(x2+x−3)−2(log⁡(x2+x−3)2+1)(x2+x−3)−2(2x+1)x(log⁡(x2+x−3)2+1)(x2+x−3)+2atan⁡(log⁡(x2+x−3))x2x\frac{- \frac{\frac{\left(2 x + 1\right)^{2}}{x^{2} + x - 3} + \frac{2 \left(2 x + 1\right)^{2} \log{\left(x^{2} + x - 3 \right)}}{\left(\log{\left(x^{2} + x - 3 \right)}^{2} + 1\right) \left(x^{2} + x - 3\right)} - 2}{\left(\log{\left(x^{2} + x - 3 \right)}^{2} + 1\right) \left(x^{2} + x - 3\right)} - \frac{2 \left(2 x + 1\right)}{x \left(\log{\left(x^{2} + x - 3 \right)}^{2} + 1\right) \left(x^{2} + x - 3\right)} + \frac{2 \operatorname{atan}{\left(\log{\left(x^{2} + x - 3 \right)} \right)}}{x^{2}}}{x}
Simplificar
Tercera derivada [src] 
                                         /               2          /          2\                           2                               2    /          2\                      2    2/          2\    \                                                                                                          
                                         |      (1 + 2*x)      6*log\-3 + x + x /                  (1 + 2*x)                     3*(1 + 2*x) *log\-3 + x + x /           4*(1 + 2*x) *log \-3 + x + x /    |     /               2                  2    /          2\    \                                           
                             2*(1 + 2*x)*|-3 + ----------- - --------------------- - ------------------------------------- + ------------------------------------- + --------------------------------------|     |      (1 + 2*x)        2*(1 + 2*x) *log\-3 + x + x /    |                                           
                                         |               2          2/          2\   /       2/          2\\ /          2\   /       2/          2\\ /          2\                          2              |   3*|-2 + ----------- + -------------------------------------|                                           
        /   /          2\\               |     -3 + x + x    1 + log \-3 + x + x /   \1 + log \-3 + x + x //*\-3 + x + x /   \1 + log \-3 + x + x //*\-3 + x + x /   /       2/          2\\  /          2\|     |               2   /       2/          2\\ /          2\|                                           
  6*atan\log\-3 + x + x //               \                                                                                                                           \1 + log \-3 + x + x // *\-3 + x + x //     \     -3 + x + x    \1 + log \-3 + x + x //*\-3 + x + x //                 6*(1 + 2*x)               
- ------------------------ + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------ + ----------------------------------------
              3                                                                                                                        2                                                                                   /       2/          2\\ /          2\               2 /       2/          2\\ /          2\
             x                                                                                    /       2/          2\\ /          2\                                                                                  x*\1 + log \-3 + x + x //*\-3 + x + x /              x *\1 + log \-3 + x + x //*\-3 + x + x /
                                                                                                  \1 + log \-3 + x + x //*\-3 + x + x /                                                                                                                                                                               
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                                                                                                                                                          x
2(2x+1)((2x+1)2x2+x−3+3(2x+1)2log⁡(x2+x−3)(log⁡(x2+x−3)2+1)(x2+x−3)−(2x+1)2(log⁡(x2+x−3)2+1)(x2+x−3)+4(2x+1)2log⁡(x2+x−3)2(log⁡(x2+x−3)2+1)2(x2+x−3)−3−6log⁡(x2+x−3)log⁡(x2+x−3)2+1)(log⁡(x2+x−3)2+1)(x2+x−3)2+3((2x+1)2x2+x−3+2(2x+1)2log⁡(x2+x−3)(log⁡(x2+x−3)2+1)(x2+x−3)−2)x(log⁡(x2+x−3)2+1)(x2+x−3)+6(2x+1)x2(log⁡(x2+x−3)2+1)(x2+x−3)−6atan⁡(log⁡(x2+x−3))x3x\frac{\frac{2 \left(2 x + 1\right) \left(\frac{\left(2 x + 1\right)^{2}}{x^{2} + x - 3} + \frac{3 \left(2 x + 1\right)^{2} \log{\left(x^{2} + x - 3 \right)}}{\left(\log{\left(x^{2} + x - 3 \right)}^{2} + 1\right) \left(x^{2} + x - 3\right)} - \frac{\left(2 x + 1\right)^{2}}{\left(\log{\left(x^{2} + x - 3 \right)}^{2} + 1\right) \left(x^{2} + x - 3\right)} + \frac{4 \left(2 x + 1\right)^{2} \log{\left(x^{2} + x - 3 \right)}^{2}}{\left(\log{\left(x^{2} + x - 3 \right)}^{2} + 1\right)^{2} \left(x^{2} + x - 3\right)} - 3 - \frac{6 \log{\left(x^{2} + x - 3 \right)}}{\log{\left(x^{2} + x - 3 \right)}^{2} + 1}\right)}{\left(\log{\left(x^{2} + x - 3 \right)}^{2} + 1\right) \left(x^{2} + x - 3\right)^{2}} + \frac{3 \left(\frac{\left(2 x + 1\right)^{2}}{x^{2} + x - 3} + \frac{2 \left(2 x + 1\right)^{2} \log{\left(x^{2} + x - 3 \right)}}{\left(\log{\left(x^{2} + x - 3 \right)}^{2} + 1\right) \left(x^{2} + x - 3\right)} - 2\right)}{x \left(\log{\left(x^{2} + x - 3 \right)}^{2} + 1\right) \left(x^{2} + x - 3\right)} + \frac{6 \left(2 x + 1\right)}{x^{2} \left(\log{\left(x^{2} + x - 3 \right)}^{2} + 1\right) \left(x^{2} + x - 3\right)} - \frac{6 \operatorname{atan}{\left(\log{\left(x^{2} + x - 3 \right)} \right)}}{x^{3}}}{x}
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Gráfico
Derivada de z=arctg*(ln*(x^2+x-3))/x
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