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y=arctan(x^2)/(1-x^2)+2lg(x/sinx)
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  • Derivada de:
  • Derivada de e^x*sin(x) Derivada de e^x*sin(x)
  • Derivada de x!
  • Derivada de e^x*x^3 Derivada de e^x*x^3
  • Derivada de e^x/x^2 Derivada de e^x/x^2
  • Expresiones idénticas

  • y=arctan(x^ dos)/(uno -x^ dos)+2lg(x/sinx)
  • y es igual a arc tangente de (x al cuadrado ) dividir por (1 menos x al cuadrado ) más 2lg(x dividir por seno de x)
  • y es igual a arc tangente de (x en el grado dos) dividir por (uno menos x en el grado dos) más 2lg(x dividir por seno de x)
  • y=arctan(x2)/(1-x2)+2lg(x/sinx)
  • y=arctanx2/1-x2+2lgx/sinx
  • y=arctan(x²)/(1-x²)+2lg(x/sinx)
  • y=arctan(x en el grado 2)/(1-x en el grado 2)+2lg(x/sinx)
  • y=arctanx^2/1-x^2+2lgx/sinx
  • y=arctan(x^2) dividir por (1-x^2)+2lg(x dividir por sinx)
  • Expresiones semejantes

  • y=arctan(x^2)/(1+x^2)+2lg(x/sinx)
  • y=arctan(x^2)/(1-x^2)-2lg(x/sinx)

Derivada de y=arctan(x^2)/(1-x^2)+2lg(x/sinx)

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
    / 2\                
atan\x /        /  x   \
-------- + 2*log|------|
      2         \sin(x)/
 1 - x                  
$$2 \log{\left(\frac{x}{\sin{\left(x \right)}} \right)} + \frac{\operatorname{atan}{\left(x^{2} \right)}}{1 - x^{2}}$$
atan(x^2)/(1 - x^2) + 2*log(x/sin(x))
Gráfica
Primera derivada [src]
                                     /  1      x*cos(x)\       
                                   2*|------ - --------|*sin(x)
                            / 2\     |sin(x)      2    |       
       2*x          2*x*atan\x /     \         sin (x) /       
----------------- + ------------ + ----------------------------
/     4\ /     2\            2                  x              
\1 + x /*\1 - x /    /     2\                                  
                     \1 - x /                                  
$$\frac{2 x}{\left(1 - x^{2}\right) \left(x^{4} + 1\right)} + \frac{2 x \operatorname{atan}{\left(x^{2} \right)}}{\left(1 - x^{2}\right)^{2}} + \frac{2 \left(- \frac{x \cos{\left(x \right)}}{\sin^{2}{\left(x \right)}} + \frac{1}{\sin{\left(x \right)}}\right) \sin{\left(x \right)}}{x}$$
Segunda derivada [src]
  /                      2                                                                                                                                          \
  |    2*cos(x)   2*x*cos (x)                                                                                                                                       |
  |x - -------- + -----------        x*cos(x)                                                                                                 /     x*cos(x)\       |
  |     sin(x)         2        -1 + --------        / 2\                            2     / 2\              2                     4          |-1 + --------|*cos(x)|
  |                 sin (x)           sin(x)     atan\x /            1            4*x *atan\x /           4*x                   4*x           \      sin(x) /       |
2*|-------------------------- + ------------- + ---------- - ------------------ - ------------- + ------------------- + ------------------- - ----------------------|
  |            x                       2                 2   /     4\ /      2\              3                      2           2                    x*sin(x)       |
  |                                   x         /      2\    \1 + x /*\-1 + x /     /      2\     /     4\ /      2\    /     4\  /      2\                         |
  \                                             \-1 + x /                           \-1 + x /     \1 + x /*\-1 + x /    \1 + x / *\-1 + x /                         /
$$2 \left(\frac{4 x^{4}}{\left(x^{2} - 1\right) \left(x^{4} + 1\right)^{2}} + \frac{4 x^{2}}{\left(x^{2} - 1\right)^{2} \left(x^{4} + 1\right)} - \frac{4 x^{2} \operatorname{atan}{\left(x^{2} \right)}}{\left(x^{2} - 1\right)^{3}} - \frac{1}{\left(x^{2} - 1\right) \left(x^{4} + 1\right)} + \frac{\operatorname{atan}{\left(x^{2} \right)}}{\left(x^{2} - 1\right)^{2}} - \frac{\left(\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} - 1\right) \cos{\left(x \right)}}{x \sin{\left(x \right)}} + \frac{x + \frac{2 x \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} - \frac{2 \cos{\left(x \right)}}{\sin{\left(x \right)}}}{x} + \frac{\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} - 1}{x^{2}}\right)$$
Tercera derivada [src]
  /                          2                          3                            /                      2   \                                                                                                                                                     /                      2   \                                  \
  |                     6*cos (x)   5*x*cos(x)   6*x*cos (x)                         |    2*cos(x)   2*x*cos (x)|                                                                                                                                                     |    2*cos(x)   2*x*cos (x)|                                  |
  |     x*cos(x)   -3 - --------- + ---------- + -----------     /     x*cos(x)\   2*|x - -------- + -----------|                                                                                                                                                   2*|x - -------- + -----------|*cos(x)     /     x*cos(x)\       |
  |-1 + --------            2         sin(x)          3        2*|-1 + --------|     |     sin(x)         2     |              7                     3                     5                    / 2\                                    3              3     / 2\     |     sin(x)         2     |          2*|-1 + --------|*cos(x)|
  |      sin(x)          sin (x)                   sin (x)       \      sin(x) /     \                 sin (x)  /          32*x                  24*x                  24*x            12*x*atan\x /           12*x                 20*x           24*x *atan\x /     \                 sin (x)  /            \      sin(x) /       |
2*|------------- - ----------------------------------------- - ----------------- - ------------------------------ - ------------------- - ------------------- - -------------------- - ------------- + ------------------- + ------------------- + -------------- + ------------------------------------- + ------------------------|
  |      x                             x                                3                         2                         3                               3           2          2              3                      2           2                        4                    x*sin(x)                         2               |
  |                                                                    x                         x                  /     4\  /      2\   /     4\ /      2\    /     4\  /      2\      /      2\     /     4\ /      2\    /     4\  /      2\     /      2\                                                     x *sin(x)        |
  \                                                                                                                 \1 + x / *\-1 + x /   \1 + x /*\-1 + x /    \1 + x / *\-1 + x /      \-1 + x /     \1 + x /*\-1 + x /    \1 + x / *\-1 + x /     \-1 + x /                                                                      /
$$2 \left(- \frac{32 x^{7}}{\left(x^{2} - 1\right) \left(x^{4} + 1\right)^{3}} - \frac{24 x^{5}}{\left(x^{2} - 1\right)^{2} \left(x^{4} + 1\right)^{2}} + \frac{20 x^{3}}{\left(x^{2} - 1\right) \left(x^{4} + 1\right)^{2}} - \frac{24 x^{3}}{\left(x^{2} - 1\right)^{3} \left(x^{4} + 1\right)} + \frac{24 x^{3} \operatorname{atan}{\left(x^{2} \right)}}{\left(x^{2} - 1\right)^{4}} + \frac{12 x}{\left(x^{2} - 1\right)^{2} \left(x^{4} + 1\right)} - \frac{12 x \operatorname{atan}{\left(x^{2} \right)}}{\left(x^{2} - 1\right)^{3}} + \frac{\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} - 1}{x} + \frac{2 \left(x + \frac{2 x \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} - \frac{2 \cos{\left(x \right)}}{\sin{\left(x \right)}}\right) \cos{\left(x \right)}}{x \sin{\left(x \right)}} - \frac{\frac{5 x \cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{6 x \cos^{3}{\left(x \right)}}{\sin^{3}{\left(x \right)}} - 3 - \frac{6 \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}}{x} + \frac{2 \left(\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} - 1\right) \cos{\left(x \right)}}{x^{2} \sin{\left(x \right)}} - \frac{2 \left(x + \frac{2 x \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} - \frac{2 \cos{\left(x \right)}}{\sin{\left(x \right)}}\right)}{x^{2}} - \frac{2 \left(\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} - 1\right)}{x^{3}}\right)$$
Gráfico
Derivada de y=arctan(x^2)/(1-x^2)+2lg(x/sinx)