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Derivada de 2^-x^3
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Derivada de (2x)^1/3
Expresiones idénticas
y=sin^ diez (arcctg(x))/sin^ siete (sqrt(x))+ uno /x^ veintidós
y es igual a seno de en el grado 10(arcctg(x)) dividir por seno de en el grado 7( raíz cuadrada de (x)) más 1 dividir por x al cuadrado 2
y es igual a seno de en el grado diez (arcctg(x)) dividir por seno de en el grado siete ( raíz cuadrada de (x)) más uno dividir por x en el grado veintidós
y=sin^10(arcctg(x))/sin^7(√(x))+1/x^22
y=sin10(arcctg(x))/sin7(sqrt(x))+1/x22
y=sin10arcctgx/sin7sqrtx+1/x22
y=sin^10(arcctg(x))/sin⁷(sqrt(x))+1/x²2
y=sin en el grado 10(arcctg(x))/sin en el grado 7(sqrt(x))+1/x en el grado 22
y=sin^10arcctgx/sin^7sqrtx+1/x^22
y=sin^10(arcctg(x)) dividir por sin^7(sqrt(x))+1 dividir por x^22
Expresiones semejantes
y=sin^10(arcctg(x))/sin^7(sqrt(x))-1/x^22

Derivada de la función/ y=sin^10(arcctg(x))/sin^7(sqrt(x))+1/x^22

Derivada de y=sin^10(arcctg(x))/sin^7(sqrt(x))+1/x^22

Solución

Ha introducido [src]

   10               
sin  (acot(x))    1 
-------------- + ---
    7/  ___\      22
 sin \\/ x /     x

\frac{\sin^{10}{\left(\operatorname{acot}{\left(x \right)} \right)}}{\sin^{7}{\left(\sqrt{x} \right)}} + \frac{1}{x^{22}}

sin(acot(x))^10/sin(sqrt(x))^7 + 1/(x^22)

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

                         9                          10             /  ___\
    22             10*sin (acot(x))            7*sin  (acot(x))*cos\\/ x /
- ----- - ---------------------------------- - ---------------------------
     22        ________                                ___    8/  ___\    
  x*x         /     1   /     2\    7/  ___\       2*\/ x *sin \\/ x /    
             /  1 + -- *\1 + x /*sin \\/ x /                              
            /        2                                                    
          \/        x

- \frac{10 \sin^{9}{\left(\operatorname{acot}{\left(x \right)} \right)}}{\sqrt{1 + \frac{1}{x^{2}}} \left(x^{2} + 1\right) \sin^{7}{\left(\sqrt{x} \right)}} - \frac{22}{x x^{22}} - \frac{7 \sin^{10}{\left(\operatorname{acot}{\left(x \right)} \right)} \cos{\left(\sqrt{x} \right)}}{2 \sqrt{x} \sin^{8}{\left(\sqrt{x} \right)}}

Simplificar

Segunda derivada [src]

           10                  2/  ___\    10                         8                        10             /  ___\                   9                                      9                                9             /  ___\       
506   7*sin  (acot(x))   14*cos \\/ x /*sin  (acot(x))          90*sin (acot(x))          7*sin  (acot(x))*cos\\/ x /             10*sin (acot(x))                     20*x*sin (acot(x))                 70*sin (acot(x))*cos\\/ x /       
--- + ---------------- + ----------------------------- + ------------------------------ + --------------------------- - ----------------------------------- + ----------------------------------- + ----------------------------------------
 24          7/  ___\                 9/  ___\                            2                       3/2    8/  ___\                  3/2                             ________         2                          ________                     
x     4*x*sin \\/ x /            x*sin \\/ x /           /    1 \ /     2\     7/  ___\        4*x   *sin \\/ x /        3 /    1 \    /     2\    7/  ___\       /     1   /     2\     7/  ___\     ___     /     1   /     2\    8/  ___\
                                                         |1 + --|*\1 + x / *sin \\/ x /                                 x *|1 + --|   *\1 + x /*sin \\/ x /      /  1 + -- *\1 + x / *sin \\/ x /   \/ x *   /  1 + -- *\1 + x /*sin \\/ x /
                                                         |     2|                                                          |     2|                             /        2                                  /        2                      
                                                         \    x /                                                          \    x /                           \/        x                                 \/        x

\frac{20 x \sin^{9}{\left(\operatorname{acot}{\left(x \right)} \right)}}{\sqrt{1 + \frac{1}{x^{2}}} \left(x^{2} + 1\right)^{2} \sin^{7}{\left(\sqrt{x} \right)}} + \frac{90 \sin^{8}{\left(\operatorname{acot}{\left(x \right)} \right)}}{\left(1 + \frac{1}{x^{2}}\right) \left(x^{2} + 1\right)^{2} \sin^{7}{\left(\sqrt{x} \right)}} + \frac{7 \sin^{10}{\left(\operatorname{acot}{\left(x \right)} \right)}}{4 x \sin^{7}{\left(\sqrt{x} \right)}} + \frac{14 \sin^{10}{\left(\operatorname{acot}{\left(x \right)} \right)} \cos^{2}{\left(\sqrt{x} \right)}}{x \sin^{9}{\left(\sqrt{x} \right)}} - \frac{10 \sin^{9}{\left(\operatorname{acot}{\left(x \right)} \right)}}{x^{3} \left(1 + \frac{1}{x^{2}}\right)^{\frac{3}{2}} \left(x^{2} + 1\right) \sin^{7}{\left(\sqrt{x} \right)}} + \frac{506}{x^{24}} + \frac{70 \sin^{9}{\left(\operatorname{acot}{\left(x \right)} \right)} \cos{\left(\sqrt{x} \right)}}{\sqrt{x} \sqrt{1 + \frac{1}{x^{2}}} \left(x^{2} + 1\right) \sin^{8}{\left(\sqrt{x} \right)}} + \frac{7 \sin^{10}{\left(\operatorname{acot}{\left(x \right)} \right)} \cos{\left(\sqrt{x} \right)}}{4 x^{\frac{3}{2}} \sin^{8}{\left(\sqrt{x} \right)}}

Simplificar

Tercera derivada [src]

                10                           7                          3/  ___\    10                  2/  ___\    10                            9                            10             /  ___\         10             /  ___\                 8                              2    9                                    9                                     9                                     9                                     8                                      9                                  8             /  ___\                 2/  ___\    9                       ___    9             /  ___\               9             /  ___\                     9             /  ___\      
  12144   21*sin  (acot(x))           720*sin (acot(x))           63*cos \\/ x /*sin  (acot(x))   21*cos \\/ x /*sin  (acot(x))             20*sin (acot(x))            161*sin  (acot(x))*cos\\/ x /   21*sin  (acot(x))*cos\\/ x /        540*x*sin (acot(x))                 80*x *sin (acot(x))                     30*sin (acot(x))                      30*sin (acot(x))                      40*sin (acot(x))                     270*sin (acot(x))                      105*sin (acot(x))                  945*sin (acot(x))*cos\\/ x /          420*cos \\/ x /*sin (acot(x))        210*\/ x *sin (acot(x))*cos\\/ x /        105*sin (acot(x))*cos\\/ x /              105*sin (acot(x))*cos\\/ x /      
- ----- - ----------------- - --------------------------------- - ----------------------------- - ----------------------------- + ----------------------------------- - ----------------------------- - ---------------------------- - ------------------------------ - ----------------------------------- - ----------------------------------- + ----------------------------------- + ------------------------------------ + ---------------------------------- - -------------------------------------- - ------------------------------------ - ------------------------------------ - ----------------------------------- + ------------------------------------- - -----------------------------------------
    25        2    7/  ___\           3/2         3                      3/2    10/  ___\                  2    9/  ___\               ________         2                        3/2    8/  ___\                5/2    8/  ___\                         3                    ________         3                          5/2                                   3/2                                   3/2         2                          2         2                        ________                                               2                      ________                             ________         2                            3/2                                    ________                     
   x       8*x *sin \\/ x /   /    1 \    /     2\     7/  ___\         x   *sin  \\/ x /                 x *sin \\/ x /              /     1   /     2\     7/  ___\         8*x   *sin \\/ x /             8*x   *sin \\/ x /        /    1 \ /     2\     7/  ___\       /     1   /     2\     7/  ___\    6 /    1 \    /     2\    7/  ___\    4 /    1 \    /     2\    7/  ___\    2 /    1 \    /     2\     7/  ___\    3 /    1 \  /     2\     7/  ___\           /     1   /     2\    7/  ___\     ___ /    1 \ /     2\     8/  ___\         /     1   /     2\    9/  ___\       /     1   /     2\     8/  ___\    7/2 /    1 \    /     2\    8/  ___\      3/2     /     1   /     2\    8/  ___\
                              |1 + --|   *\1 + x / *sin \\/ x /                                                                      /  1 + -- *\1 + x / *sin \\/ x /                                                                  |1 + --|*\1 + x / *sin \\/ x /      /  1 + -- *\1 + x / *sin \\/ x /   x *|1 + --|   *\1 + x /*sin \\/ x /   x *|1 + --|   *\1 + x /*sin \\/ x /   x *|1 + --|   *\1 + x / *sin \\/ x /   x *|1 + --| *\1 + x / *sin \\/ x /   2*x*   /  1 + -- *\1 + x /*sin \\/ x /   \/ x *|1 + --|*\1 + x / *sin \\/ x /   x*   /  1 + -- *\1 + x /*sin \\/ x /      /  1 + -- *\1 + x / *sin \\/ x /   x   *|1 + --|   *\1 + x /*sin \\/ x /   2*x   *   /  1 + -- *\1 + x /*sin \\/ x /
                              |     2|                                                                                              /        2                                                                                         |     2|                           /        2                             |     2|                              |     2|                              |     2|                               |     2|                                /        2                               |     2|                             /        2                           /        2                               |     2|                                    /        2                      
                              \    x /                                                                                            \/        x                                                                                          \    x /                         \/        x                              \    x /                              \    x /                              \    x /                               \    x /                              \/        x                                \    x /                           \/        x                          \/        x                                \    x /                                  \/        x

- \frac{210 \sqrt{x} \sin^{9}{\left(\operatorname{acot}{\left(x \right)} \right)} \cos{\left(\sqrt{x} \right)}}{\sqrt{1 + \frac{1}{x^{2}}} \left(x^{2} + 1\right)^{2} \sin^{8}{\left(\sqrt{x} \right)}} - \frac{80 x^{2} \sin^{9}{\left(\operatorname{acot}{\left(x \right)} \right)}}{\sqrt{1 + \frac{1}{x^{2}}} \left(x^{2} + 1\right)^{3} \sin^{7}{\left(\sqrt{x} \right)}} - \frac{540 x \sin^{8}{\left(\operatorname{acot}{\left(x \right)} \right)}}{\left(1 + \frac{1}{x^{2}}\right) \left(x^{2} + 1\right)^{3} \sin^{7}{\left(\sqrt{x} \right)}} + \frac{20 \sin^{9}{\left(\operatorname{acot}{\left(x \right)} \right)}}{\sqrt{1 + \frac{1}{x^{2}}} \left(x^{2} + 1\right)^{2} \sin^{7}{\left(\sqrt{x} \right)}} - \frac{720 \sin^{7}{\left(\operatorname{acot}{\left(x \right)} \right)}}{\left(1 + \frac{1}{x^{2}}\right)^{\frac{3}{2}} \left(x^{2} + 1\right)^{3} \sin^{7}{\left(\sqrt{x} \right)}} - \frac{105 \sin^{9}{\left(\operatorname{acot}{\left(x \right)} \right)}}{2 x \sqrt{1 + \frac{1}{x^{2}}} \left(x^{2} + 1\right) \sin^{7}{\left(\sqrt{x} \right)}} - \frac{420 \sin^{9}{\left(\operatorname{acot}{\left(x \right)} \right)} \cos^{2}{\left(\sqrt{x} \right)}}{x \sqrt{1 + \frac{1}{x^{2}}} \left(x^{2} + 1\right) \sin^{9}{\left(\sqrt{x} \right)}} - \frac{21 \sin^{10}{\left(\operatorname{acot}{\left(x \right)} \right)}}{8 x^{2} \sin^{7}{\left(\sqrt{x} \right)}} - \frac{21 \sin^{10}{\left(\operatorname{acot}{\left(x \right)} \right)} \cos^{2}{\left(\sqrt{x} \right)}}{x^{2} \sin^{9}{\left(\sqrt{x} \right)}} + \frac{40 \sin^{9}{\left(\operatorname{acot}{\left(x \right)} \right)}}{x^{2} \left(1 + \frac{1}{x^{2}}\right)^{\frac{3}{2}} \left(x^{2} + 1\right)^{2} \sin^{7}{\left(\sqrt{x} \right)}} + \frac{270 \sin^{8}{\left(\operatorname{acot}{\left(x \right)} \right)}}{x^{3} \left(1 + \frac{1}{x^{2}}\right)^{2} \left(x^{2} + 1\right)^{2} \sin^{7}{\left(\sqrt{x} \right)}} + \frac{30 \sin^{9}{\left(\operatorname{acot}{\left(x \right)} \right)}}{x^{4} \left(1 + \frac{1}{x^{2}}\right)^{\frac{3}{2}} \left(x^{2} + 1\right) \sin^{7}{\left(\sqrt{x} \right)}} - \frac{30 \sin^{9}{\left(\operatorname{acot}{\left(x \right)} \right)}}{x^{6} \left(1 + \frac{1}{x^{2}}\right)^{\frac{5}{2}} \left(x^{2} + 1\right) \sin^{7}{\left(\sqrt{x} \right)}} - \frac{12144}{x^{25}} - \frac{945 \sin^{8}{\left(\operatorname{acot}{\left(x \right)} \right)} \cos{\left(\sqrt{x} \right)}}{\sqrt{x} \left(1 + \frac{1}{x^{2}}\right) \left(x^{2} + 1\right)^{2} \sin^{8}{\left(\sqrt{x} \right)}} - \frac{161 \sin^{10}{\left(\operatorname{acot}{\left(x \right)} \right)} \cos{\left(\sqrt{x} \right)}}{8 x^{\frac{3}{2}} \sin^{8}{\left(\sqrt{x} \right)}} - \frac{63 \sin^{10}{\left(\operatorname{acot}{\left(x \right)} \right)} \cos^{3}{\left(\sqrt{x} \right)}}{x^{\frac{3}{2}} \sin^{10}{\left(\sqrt{x} \right)}} - \frac{105 \sin^{9}{\left(\operatorname{acot}{\left(x \right)} \right)} \cos{\left(\sqrt{x} \right)}}{2 x^{\frac{3}{2}} \sqrt{1 + \frac{1}{x^{2}}} \left(x^{2} + 1\right) \sin^{8}{\left(\sqrt{x} \right)}} - \frac{21 \sin^{10}{\left(\operatorname{acot}{\left(x \right)} \right)} \cos{\left(\sqrt{x} \right)}}{8 x^{\frac{5}{2}} \sin^{8}{\left(\sqrt{x} \right)}} + \frac{105 \sin^{9}{\left(\operatorname{acot}{\left(x \right)} \right)} \cos{\left(\sqrt{x} \right)}}{x^{\frac{7}{2}} \left(1 + \frac{1}{x^{2}}\right)^{\frac{3}{2}} \left(x^{2} + 1\right) \sin^{8}{\left(\sqrt{x} \right)}}

Simplificar

Gráfico

Derivada de y=sin^10(arcctg(x))/sin^7(sqrt(x))+1/x^22

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Expresiones semejantes

Derivada de y=sin^10(arcctg(x))/sin^7(sqrt(x))+1/x^22

Gráfico:

Definida a trozos:

Solución