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log((1+sqrt(sin(x)))/(1-sqrt(sin(x))))+2*atan(sqrt(sin(x)))
Derivada de la función/ log((1+sqrt(sin(x)))/(1-sqrt(sin(x))))+2*atan(sqrt(sin(x)))

Derivada de log((1+sqrt(sin(x)))/(1-sqrt(sin(x))))+2*atan(sqrt(sin(x)))

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

Gráfico:

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Solución

Ha introducido [src] 
   /      ________\                     
   |1 + \/ sin(x) |         /  ________\
log|--------------| + 2*atan\\/ sin(x) /
   |      ________|                     
   \1 - \/ sin(x) /
log⁡(sin⁡(x)+11−sin⁡(x))+2atan⁡(sin⁡(x))\log{\left(\frac{\sqrt{\sin{\left(x \right)}} + 1}{1 - \sqrt{\sin{\left(x \right)}}} \right)} + 2 \operatorname{atan}{\left(\sqrt{\sin{\left(x \right)}} \right)} 
log((1 + sqrt(sin(x)))/(1 - sqrt(sin(x)))) + 2*atan(sqrt(sin(x)))
Gráfica
02468-8-6-4-2-1010-100100
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
                 /                                   /      ________\           \                          
/      ________\ |            cos(x)                 \1 + \/ sin(x) /*cos(x)    |                          
\1 - \/ sin(x) /*|----------------------------- + ------------------------------|                          
                 |  /      ________\   ________                     2           |                          
                 |2*\1 - \/ sin(x) /*\/ sin(x)      /      ________\    ________|                          
                 \                                2*\1 - \/ sin(x) / *\/ sin(x) /            cos(x)        
--------------------------------------------------------------------------------- + -----------------------
                                        ________                                                   ________
                                  1 + \/ sin(x)                                     (1 + sin(x))*\/ sin(x)
(1−sin⁡(x))(cos⁡(x)2(1−sin⁡(x))sin⁡(x)+(sin⁡(x)+1)cos⁡(x)2(1−sin⁡(x))2sin⁡(x))sin⁡(x)+1+cos⁡(x)(sin⁡(x)+1)sin⁡(x)\frac{\left(1 - \sqrt{\sin{\left(x \right)}}\right) \left(\frac{\cos{\left(x \right)}}{2 \left(1 - \sqrt{\sin{\left(x \right)}}\right) \sqrt{\sin{\left(x \right)}}} + \frac{\left(\sqrt{\sin{\left(x \right)}} + 1\right) \cos{\left(x \right)}}{2 \left(1 - \sqrt{\sin{\left(x \right)}}\right)^{2} \sqrt{\sin{\left(x \right)}}}\right)}{\sqrt{\sin{\left(x \right)}} + 1} + \frac{\cos{\left(x \right)}}{\left(\sin{\left(x \right)} + 1\right) \sqrt{\sin{\left(x \right)}}}
Simplificar
Segunda derivada [src] 
                                  2           ________ /      ________\               2                   2    /      ________\         2    /      ________\                                                                                                                                    
                   ________    cos (x)    2*\/ sin(x) *\1 + \/ sin(x) /          2*cos (x)             cos (x)*\1 + \/ sin(x) /    2*cos (x)*\1 + \/ sin(x) /                                                                 /           ________\                  /           ________\       
               2*\/ sin(x)  + --------- - ----------------------------- + ------------------------ - --------------------------- - --------------------------                                                            2    |     1 + \/ sin(x) |             2    |     1 + \/ sin(x) |       
                                 3/2                    ________          /       ________\          /       ________\    3/2                       2                                                                 cos (x)*|1 - ---------------|          cos (x)*|1 - ---------------|       
    ________                  sin   (x)          -1 + \/ sin(x)           \-1 + \/ sin(x) /*sin(x)   \-1 + \/ sin(x) /*sin   (x)   /       ________\                       2                          2                       |           ________|                  |           ________|       
  \/ sin(x)                                                                                                                        \-1 + \/ sin(x) / *sin(x)            cos (x)                    cos (x)                    \    -1 + \/ sin(x) /                  \    -1 + \/ sin(x) /       
- ---------- - ---------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------ - ------------------------ - ----------------------------- + -------------------------------------------
  1 + sin(x)                                                                   /      ________\                                                                             2   ________                     3/2                          2             /      ________\ /       ________\       
                                                                             4*\1 + \/ sin(x) /                                                                 (1 + sin(x)) *\/ sin(x)    2*(1 + sin(x))*sin   (x)       /      ________\            4*\1 + \/ sin(x) /*\-1 + \/ sin(x) /*sin(x)
                                                                                                                                                                                                                        4*\1 + \/ sin(x) / *sin(x)
−(1−sin⁡(x)+1sin⁡(x)−1)cos⁡2(x)4(sin⁡(x)+1)2sin⁡(x)+(1−sin⁡(x)+1sin⁡(x)−1)cos⁡2(x)4(sin⁡(x)−1)(sin⁡(x)+1)sin⁡(x)−sin⁡(x)sin⁡(x)+1−cos⁡2(x)2(sin⁡(x)+1)sin⁡32(x)−cos⁡2(x)(sin⁡(x)+1)2sin⁡(x)−2sin⁡(x)+cos⁡2(x)sin⁡32(x)−2(sin⁡(x)+1)sin⁡(x)sin⁡(x)−1−(sin⁡(x)+1)cos⁡2(x)(sin⁡(x)−1)sin⁡32(x)+2cos⁡2(x)(sin⁡(x)−1)sin⁡(x)−2(sin⁡(x)+1)cos⁡2(x)(sin⁡(x)−1)2sin⁡(x)4(sin⁡(x)+1)- \frac{\left(1 - \frac{\sqrt{\sin{\left(x \right)}} + 1}{\sqrt{\sin{\left(x \right)}} - 1}\right) \cos^{2}{\left(x \right)}}{4 \left(\sqrt{\sin{\left(x \right)}} + 1\right)^{2} \sin{\left(x \right)}} + \frac{\left(1 - \frac{\sqrt{\sin{\left(x \right)}} + 1}{\sqrt{\sin{\left(x \right)}} - 1}\right) \cos^{2}{\left(x \right)}}{4 \left(\sqrt{\sin{\left(x \right)}} - 1\right) \left(\sqrt{\sin{\left(x \right)}} + 1\right) \sin{\left(x \right)}} - \frac{\sqrt{\sin{\left(x \right)}}}{\sin{\left(x \right)} + 1} - \frac{\cos^{2}{\left(x \right)}}{2 \left(\sin{\left(x \right)} + 1\right) \sin^{\frac{3}{2}}{\left(x \right)}} - \frac{\cos^{2}{\left(x \right)}}{\left(\sin{\left(x \right)} + 1\right)^{2} \sqrt{\sin{\left(x \right)}}} - \frac{2 \sqrt{\sin{\left(x \right)}} + \frac{\cos^{2}{\left(x \right)}}{\sin^{\frac{3}{2}}{\left(x \right)}} - \frac{2 \left(\sqrt{\sin{\left(x \right)}} + 1\right) \sqrt{\sin{\left(x \right)}}}{\sqrt{\sin{\left(x \right)}} - 1} - \frac{\left(\sqrt{\sin{\left(x \right)}} + 1\right) \cos^{2}{\left(x \right)}}{\left(\sqrt{\sin{\left(x \right)}} - 1\right) \sin^{\frac{3}{2}}{\left(x \right)}} + \frac{2 \cos^{2}{\left(x \right)}}{\left(\sqrt{\sin{\left(x \right)}} - 1\right) \sin{\left(x \right)}} - \frac{2 \left(\sqrt{\sin{\left(x \right)}} + 1\right) \cos^{2}{\left(x \right)}}{\left(\sqrt{\sin{\left(x \right)}} - 1\right)^{2} \sin{\left(x \right)}}}{4 \left(\sqrt{\sin{\left(x \right)}} + 1\right)}
Simplificar
Tercera derivada [src] 
/                                                                                                    /      ________\        2             /      ________\                     2                            2                      2    /      ________\         2    /      ________\         2    /      ________\                                                                                                                  2           ________ /      ________\               2                   2    /      ________\         2    /      ________\                                                 2           ________ /      ________\               2                   2    /      ________\         2    /      ________\                                                                                                                                                                 \       
|                                                       ________       2               12         12*\1 + \/ sin(x) /   3*cos (x)        2*\1 + \/ sin(x) /                6*cos (x)                    6*cos (x)              6*cos (x)*\1 + \/ sin(x) /    6*cos (x)*\1 + \/ sin(x) /    3*cos (x)*\1 + \/ sin(x) /                                                                           ________                ________    cos (x)    2*\/ sin(x) *\1 + \/ sin(x) /          2*cos (x)             cos (x)*\1 + \/ sin(x) /    2*cos (x)*\1 + \/ sin(x) /                                  ________    cos (x)    2*\/ sin(x) *\1 + \/ sin(x) /          2*cos (x)             cos (x)*\1 + \/ sin(x) /    2*cos (x)*\1 + \/ sin(x) /           /           ________\           /           ________\                    /           ________\                           /           ________\        |       
|                                                 1 + \/ sin(x)    ---------- + --------------- - ------------------- + --------- - ---------------------------- + ------------------------- + ---------------------------- - ---------------------------- - -------------------------- - ---------------------------                                                                     1 + \/ sin(x)             2*\/ sin(x)  + --------- - ----------------------------- + ------------------------ - --------------------------- - --------------------------                              2*\/ sin(x)  + --------- - ----------------------------- + ------------------------ - --------------------------- - --------------------------      2    |     1 + \/ sin(x) |      2    |     1 + \/ sin(x) |               2    |     1 + \/ sin(x) |                      2    |     1 + \/ sin(x) |        |       
|                                            1 - ---------------     ________          ________                     2      5/2      /       ________\   ________   /       ________\    2                       2                              3                              2           /       ________\    5/2                                                                   1 - ---------------                              3/2                    ________          /       ________\          /       ________\    3/2                       2                                                        3/2                    ________          /       ________\          /       ________\    3/2                       2           cos (x)*|1 - ---------------|   cos (x)*|1 - ---------------|            cos (x)*|1 - ---------------|                   cos (x)*|1 - ---------------|        |       
|                                 ________              ________   \/ sin(x)    -1 + \/ sin(x)     /       ________\    sin   (x)   \-1 + \/ sin(x) /*\/ sin(x)    \-1 + \/ sin(x) /*sin (x)   /       ________\     3/2      /       ________\     3/2      /       ________\     2      \-1 + \/ sin(x) /*sin   (x)              2                          2                                 ________                           sin   (x)          -1 + \/ sin(x)           \-1 + \/ sin(x) /*sin(x)   \-1 + \/ sin(x) /*sin   (x)   /       ________\                        2                             sin   (x)          -1 + \/ sin(x)           \-1 + \/ sin(x) /*sin(x)   \-1 + \/ sin(x) /*sin   (x)   /       ________\                    |           ________|           |           ________|                    |           ________|                           |           ________|        |       
|            1                3*\/ sin(x)        -1 + \/ sin(x)                                    \-1 + \/ sin(x) /                                                                           \-1 + \/ sin(x) / *sin   (x)   \-1 + \/ sin(x) / *sin   (x)   \-1 + \/ sin(x) / *sin (x)                                         cos (x)                  2*cos (x)                       -1 + \/ sin(x)                                                                                                                                 \-1 + \/ sin(x) / *sin(x)           3*cos (x)                                                                                                                               \-1 + \/ sin(x) / *sin(x)            \    -1 + \/ sin(x) /           \    -1 + \/ sin(x) /                    \    -1 + \/ sin(x) /                           \    -1 + \/ sin(x) /        |       
|------------------------- + ------------- + ------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------- + ------------------------ - ------------------------------------ + ---------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------ - ---------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------- + ----------------------------- - ----------------------------------------------- - --------------------------------------------|*cos(x)
|                 ________               2                     2                                                                                                                     /      ________\                                                                                                                               2    3/2                  3   ________     /      ________\ /       ________\                                                                             2                                                                                        5/2                                                       /      ________\ /       ________\   ________                                                                     3                                2                              2                                 /      ________\ /       ________\    2   |       
|2*(1 + sin(x))*\/ sin(x)    (1 + sin(x))      /      ________\                                                                                                                    8*\1 + \/ sin(x) /                                                                                                                   (1 + sin(x)) *sin   (x)   (1 + sin(x)) *\/ sin(x)    4*\1 + \/ sin(x) /*\-1 + \/ sin(x) /                                                             /      ________\    ________                                                           4*(1 + sin(x))*sin   (x)                                                  4*\1 + \/ sin(x) /*\-1 + \/ sin(x) /*\/ sin(x)                                                      /      ________\     3/2         /      ________\     2         /      ________\  /       ________\    3/2      8*\1 + \/ sin(x) /*\-1 + \/ sin(x) /*sin (x)|       
\                                            4*\1 + \/ sin(x) /                                                                                                                                                                                                                                                                                                                                                                                                             4*\1 + \/ sin(x) / *\/ sin(x)                                                                                                                                                                                                                                        4*\1 + \/ sin(x) / *sin   (x)    8*\1 + \/ sin(x) / *sin (x)    4*\1 + \/ sin(x) / *\-1 + \/ sin(x) /*sin   (x)                                               /
(1−sin⁡(x)+1sin⁡(x)−14(sin⁡(x)+1)2+(1−sin⁡(x)+1sin⁡(x)−1)cos⁡2(x)8(sin⁡(x)+1)2sin⁡2(x)+(1−sin⁡(x)+1sin⁡(x)−1)cos⁡2(x)4(sin⁡(x)+1)3sin⁡32(x)−1−sin⁡(x)+1sin⁡(x)−14(sin⁡(x)−1)(sin⁡(x)+1)−(1−sin⁡(x)+1sin⁡(x)−1)cos⁡2(x)8(sin⁡(x)−1)(sin⁡(x)+1)sin⁡2(x)−(1−sin⁡(x)+1sin⁡(x)−1)cos⁡2(x)4(sin⁡(x)−1)(sin⁡(x)+1)2sin⁡32(x)+12(sin⁡(x)+1)sin⁡(x)+3cos⁡2(x)4(sin⁡(x)+1)sin⁡52(x)+3sin⁡(x)(sin⁡(x)+1)2+cos⁡2(x)(sin⁡(x)+1)2sin⁡32(x)+2cos⁡2(x)(sin⁡(x)+1)3sin⁡(x)+2sin⁡(x)+3cos⁡2(x)sin⁡52(x)−2(sin⁡(x)+1)(sin⁡(x)−1)sin⁡(x)−3(sin⁡(x)+1)cos⁡2(x)(sin⁡(x)−1)sin⁡52(x)+12sin⁡(x)−1+6cos⁡2(x)(sin⁡(x)−1)sin⁡2(x)−12(sin⁡(x)+1)(sin⁡(x)−1)2−6(sin⁡(x)+1)cos⁡2(x)(sin⁡(x)−1)2sin⁡2(x)+6cos⁡2(x)(sin⁡(x)−1)2sin⁡32(x)−6(sin⁡(x)+1)cos⁡2(x)(sin⁡(x)−1)3sin⁡32(x)8(sin⁡(x)+1)+2sin⁡(x)+cos⁡2(x)sin⁡32(x)−2(sin⁡(x)+1)sin⁡(x)sin⁡(x)−1−(sin⁡(x)+1)cos⁡2(x)(sin⁡(x)−1)sin⁡32(x)+2cos⁡2(x)(sin⁡(x)−1)sin⁡(x)−2(sin⁡(x)+1)cos⁡2(x)(sin⁡(x)−1)2sin⁡(x)4(sin⁡(x)+1)2sin⁡(x)−2sin⁡(x)+cos⁡2(x)sin⁡32(x)−2(sin⁡(x)+1)sin⁡(x)sin⁡(x)−1−(sin⁡(x)+1)cos⁡2(x)(sin⁡(x)−1)sin⁡32(x)+2cos⁡2(x)(sin⁡(x)−1)sin⁡(x)−2(sin⁡(x)+1)cos⁡2(x)(sin⁡(x)−1)2sin⁡(x)4(sin⁡(x)−1)(sin⁡(x)+1)sin⁡(x))cos⁡(x)\left(\frac{1 - \frac{\sqrt{\sin{\left(x \right)}} + 1}{\sqrt{\sin{\left(x \right)}} - 1}}{4 \left(\sqrt{\sin{\left(x \right)}} + 1\right)^{2}} + \frac{\left(1 - \frac{\sqrt{\sin{\left(x \right)}} + 1}{\sqrt{\sin{\left(x \right)}} - 1}\right) \cos^{2}{\left(x \right)}}{8 \left(\sqrt{\sin{\left(x \right)}} + 1\right)^{2} \sin^{2}{\left(x \right)}} + \frac{\left(1 - \frac{\sqrt{\sin{\left(x \right)}} + 1}{\sqrt{\sin{\left(x \right)}} - 1}\right) \cos^{2}{\left(x \right)}}{4 \left(\sqrt{\sin{\left(x \right)}} + 1\right)^{3} \sin^{\frac{3}{2}}{\left(x \right)}} - \frac{1 - \frac{\sqrt{\sin{\left(x \right)}} + 1}{\sqrt{\sin{\left(x \right)}} - 1}}{4 \left(\sqrt{\sin{\left(x \right)}} - 1\right) \left(\sqrt{\sin{\left(x \right)}} + 1\right)} - \frac{\left(1 - \frac{\sqrt{\sin{\left(x \right)}} + 1}{\sqrt{\sin{\left(x \right)}} - 1}\right) \cos^{2}{\left(x \right)}}{8 \left(\sqrt{\sin{\left(x \right)}} - 1\right) \left(\sqrt{\sin{\left(x \right)}} + 1\right) \sin^{2}{\left(x \right)}} - \frac{\left(1 - \frac{\sqrt{\sin{\left(x \right)}} + 1}{\sqrt{\sin{\left(x \right)}} - 1}\right) \cos^{2}{\left(x \right)}}{4 \left(\sqrt{\sin{\left(x \right)}} - 1\right) \left(\sqrt{\sin{\left(x \right)}} + 1\right)^{2} \sin^{\frac{3}{2}}{\left(x \right)}} + \frac{1}{2 \left(\sin{\left(x \right)} + 1\right) \sqrt{\sin{\left(x \right)}}} + \frac{3 \cos^{2}{\left(x \right)}}{4 \left(\sin{\left(x \right)} + 1\right) \sin^{\frac{5}{2}}{\left(x \right)}} + \frac{3 \sqrt{\sin{\left(x \right)}}}{\left(\sin{\left(x \right)} + 1\right)^{2}} + \frac{\cos^{2}{\left(x \right)}}{\left(\sin{\left(x \right)} + 1\right)^{2} \sin^{\frac{3}{2}}{\left(x \right)}} + \frac{2 \cos^{2}{\left(x \right)}}{\left(\sin{\left(x \right)} + 1\right)^{3} \sqrt{\sin{\left(x \right)}}} + \frac{\frac{2}{\sqrt{\sin{\left(x \right)}}} + \frac{3 \cos^{2}{\left(x \right)}}{\sin^{\frac{5}{2}}{\left(x \right)}} - \frac{2 \left(\sqrt{\sin{\left(x \right)}} + 1\right)}{\left(\sqrt{\sin{\left(x \right)}} - 1\right) \sqrt{\sin{\left(x \right)}}} - \frac{3 \left(\sqrt{\sin{\left(x \right)}} + 1\right) \cos^{2}{\left(x \right)}}{\left(\sqrt{\sin{\left(x \right)}} - 1\right) \sin^{\frac{5}{2}}{\left(x \right)}} + \frac{12}{\sqrt{\sin{\left(x \right)}} - 1} + \frac{6 \cos^{2}{\left(x \right)}}{\left(\sqrt{\sin{\left(x \right)}} - 1\right) \sin^{2}{\left(x \right)}} - \frac{12 \left(\sqrt{\sin{\left(x \right)}} + 1\right)}{\left(\sqrt{\sin{\left(x \right)}} - 1\right)^{2}} - \frac{6 \left(\sqrt{\sin{\left(x \right)}} + 1\right) \cos^{2}{\left(x \right)}}{\left(\sqrt{\sin{\left(x \right)}} - 1\right)^{2} \sin^{2}{\left(x \right)}} + \frac{6 \cos^{2}{\left(x \right)}}{\left(\sqrt{\sin{\left(x \right)}} - 1\right)^{2} \sin^{\frac{3}{2}}{\left(x \right)}} - \frac{6 \left(\sqrt{\sin{\left(x \right)}} + 1\right) \cos^{2}{\left(x \right)}}{\left(\sqrt{\sin{\left(x \right)}} - 1\right)^{3} \sin^{\frac{3}{2}}{\left(x \right)}}}{8 \left(\sqrt{\sin{\left(x \right)}} + 1\right)} + \frac{2 \sqrt{\sin{\left(x \right)}} + \frac{\cos^{2}{\left(x \right)}}{\sin^{\frac{3}{2}}{\left(x \right)}} - \frac{2 \left(\sqrt{\sin{\left(x \right)}} + 1\right) \sqrt{\sin{\left(x \right)}}}{\sqrt{\sin{\left(x \right)}} - 1} - \frac{\left(\sqrt{\sin{\left(x \right)}} + 1\right) \cos^{2}{\left(x \right)}}{\left(\sqrt{\sin{\left(x \right)}} - 1\right) \sin^{\frac{3}{2}}{\left(x \right)}} + \frac{2 \cos^{2}{\left(x \right)}}{\left(\sqrt{\sin{\left(x \right)}} - 1\right) \sin{\left(x \right)}} - \frac{2 \left(\sqrt{\sin{\left(x \right)}} + 1\right) \cos^{2}{\left(x \right)}}{\left(\sqrt{\sin{\left(x \right)}} - 1\right)^{2} \sin{\left(x \right)}}}{4 \left(\sqrt{\sin{\left(x \right)}} + 1\right)^{2} \sqrt{\sin{\left(x \right)}}} - \frac{2 \sqrt{\sin{\left(x \right)}} + \frac{\cos^{2}{\left(x \right)}}{\sin^{\frac{3}{2}}{\left(x \right)}} - \frac{2 \left(\sqrt{\sin{\left(x \right)}} + 1\right) \sqrt{\sin{\left(x \right)}}}{\sqrt{\sin{\left(x \right)}} - 1} - \frac{\left(\sqrt{\sin{\left(x \right)}} + 1\right) \cos^{2}{\left(x \right)}}{\left(\sqrt{\sin{\left(x \right)}} - 1\right) \sin^{\frac{3}{2}}{\left(x \right)}} + \frac{2 \cos^{2}{\left(x \right)}}{\left(\sqrt{\sin{\left(x \right)}} - 1\right) \sin{\left(x \right)}} - \frac{2 \left(\sqrt{\sin{\left(x \right)}} + 1\right) \cos^{2}{\left(x \right)}}{\left(\sqrt{\sin{\left(x \right)}} - 1\right)^{2} \sin{\left(x \right)}}}{4 \left(\sqrt{\sin{\left(x \right)}} - 1\right) \left(\sqrt{\sin{\left(x \right)}} + 1\right) \sqrt{\sin{\left(x \right)}}}\right) \cos{\left(x \right)}
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Gráfico
Derivada de log((1+sqrt(sin(x)))/(1-sqrt(sin(x))))+2*atan(sqrt(sin(x)))
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