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asin(x)/sqrt(1-x^2)+tan(x)*cot((x-1)/(x))
Derivada de la función/ asin(x)/sqrt(1-x^2)+tan(x)*cot((x-1)/(x))

Derivada de asin(x)/sqrt(1-x^2)+tan(x)*cot((x-1)/(x))

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

Gráfico:

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Solución

Ha introducido [src] 
  asin(x)               /x - 1\
----------- + tan(x)*cot|-----|
   ________             \  x  /
  /      2                     
\/  1 - x
tan⁡(x)cot⁡(x−1x)+asin⁡(x)1−x2\tan{\left(x \right)} \cot{\left(\frac{x - 1}{x} \right)} + \frac{\operatorname{asin}{\left(x \right)}}{\sqrt{1 - x^{2}}} 
asin(x)/sqrt(1 - x^2) + tan(x)*cot((x - 1)/x)
Gráfica
02468-8-6-4-2-1010-250250
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
           1              /       2   \    /x - 1\    x*asin(x)    /        2/x - 1\\ /1   x - 1\       
----------------------- + \1 + tan (x)/*cot|-----| + ----------- + |-1 - cot |-----||*|- - -----|*tan(x)
   ________    ________                    \  x  /           3/2   \         \  x  // |x      2 |       
  /      2    /      2                               /     2\                         \      x  /       
\/  1 - x  *\/  1 - x                                \1 - x /
xasin⁡(x)(1−x2)32+(1x−x−1x2)(−cot⁡2(x−1x)−1)tan⁡(x)+(tan⁡2(x)+1)cot⁡(x−1x)+11−x21−x2\frac{x \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \left(\frac{1}{x} - \frac{x - 1}{x^{2}}\right) \left(- \cot^{2}{\left(\frac{x - 1}{x} \right)} - 1\right) \tan{\left(x \right)} + \left(\tan^{2}{\left(x \right)} + 1\right) \cot{\left(\frac{x - 1}{x} \right)} + \frac{1}{\sqrt{1 - x^{2}} \sqrt{1 - x^{2}}}
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Segunda derivada [src] 
                                                                                                                                                                                          2                                      
                                                                                 /       2/-1 + x\\ /       2   \ /    -1 + x\     /       2/-1 + x\\ /    -1 + x\            /    -1 + x\  /       2/-1 + x\\    /-1 + x\       
                                                                   2           2*|1 + cot |------||*\1 + tan (x)/*|1 - ------|   2*|1 + cot |------||*|1 - ------|*tan(x)   2*|1 - ------| *|1 + cot |------||*cot|------|*tan(x)
  asin(x)        3*x         /       2   \    /-1 + x\          3*x *asin(x)     \        \  x   //               \      x   /     \        \  x   // \      x   /            \      x   /  \        \  x   //    \  x   /       
----------- + ---------- + 2*\1 + tan (x)/*cot|------|*tan(x) + ------------ - ----------------------------------------------- + ---------------------------------------- + -----------------------------------------------------
        3/2            2                      \  x   /                  5/2                           x                                              2                                                 2                         
/     2\      /      2\                                         /     2\                                                                            x                                                 x                          
\1 - x /      \-1 + x /                                         \1 - x /
3x2asin⁡(x)(1−x2)52+3x(x2−1)2+2(tan⁡2(x)+1)tan⁡(x)cot⁡(x−1x)+asin⁡(x)(1−x2)32−2(1−x−1x)(tan⁡2(x)+1)(cot⁡2(x−1x)+1)x+2(1−x−1x)2(cot⁡2(x−1x)+1)tan⁡(x)cot⁡(x−1x)x2+2(1−x−1x)(cot⁡2(x−1x)+1)tan⁡(x)x2\frac{3 x^{2} \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{3 x}{\left(x^{2} - 1\right)^{2}} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} \cot{\left(\frac{x - 1}{x} \right)} + \frac{\operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{2 \left(1 - \frac{x - 1}{x}\right) \left(\tan^{2}{\left(x \right)} + 1\right) \left(\cot^{2}{\left(\frac{x - 1}{x} \right)} + 1\right)}{x} + \frac{2 \left(1 - \frac{x - 1}{x}\right)^{2} \left(\cot^{2}{\left(\frac{x - 1}{x} \right)} + 1\right) \tan{\left(x \right)} \cot{\left(\frac{x - 1}{x} \right)}}{x^{2}} + \frac{2 \left(1 - \frac{x - 1}{x}\right) \left(\cot^{2}{\left(\frac{x - 1}{x} \right)} + 1\right) \tan{\left(x \right)}}{x^{2}}
Simplificar
Tercera derivada [src] 
                                                                                                                                                                                            2             3                                                                           2                                                                                                                3                                                        2                                             
                                                                                                                               /       2/-1 + x\\ /    -1 + x\            /       2/-1 + x\\  /    -1 + x\             /       2/-1 + x\\ /       2   \ /    -1 + x\      /    -1 + x\  /       2/-1 + x\\    /-1 + x\            /       2/-1 + x\\ /       2   \ /    -1 + x\            /    -1 + x\     2/-1 + x\ /       2/-1 + x\\            /    -1 + x\  /       2/-1 + x\\ /       2   \    /-1 + x\
                   2                     2                                                                       3           6*|1 + cot |------||*|1 - ------|*tan(x)   2*|1 + cot |------|| *|1 - ------| *tan(x)   6*|1 + cot |------||*\1 + tan (x)/*|1 - ------|   12*|1 - ------| *|1 + cot |------||*cot|------|*tan(x)   6*|1 + cot |------||*\1 + tan (x)/*|1 - ------|*tan(x)   4*|1 - ------| *cot |------|*|1 + cot |------||*tan(x)   6*|1 - ------| *|1 + cot |------||*\1 + tan (x)/*cot|------|
    4          15*x         /       2   \     /-1 + x\        2    /       2   \    /-1 + x\   9*x*asin(x)   15*x *asin(x)     \        \  x   // \      x   /            \        \  x   //  \      x   /             \        \  x   //               \      x   /      \      x   /  \        \  x   //    \  x   /            \        \  x   //               \      x   /            \      x   /      \  x   / \        \  x   //            \      x   /  \        \  x   //                  \  x   /
---------- - ---------- + 2*\1 + tan (x)/ *cot|------| + 4*tan (x)*\1 + tan (x)/*cot|------| + ----------- + ------------- - ---------------------------------------- - ------------------------------------------ + ----------------------------------------------- - ------------------------------------------------------ - ------------------------------------------------------ - ------------------------------------------------------ + ------------------------------------------------------------
         2            3                       \  x   /                              \  x   /           5/2            7/2                        3                                           3                                               2                                                    3                                                       x                                                         3                                                           2                             
/      2\    /      2\                                                                         /     2\       /     2\                          x                                           x                                               x                                                    x                                                                                                                 x                                                           x                              
\-1 + x /    \-1 + x /                                                                         \1 - x /       \1 - x /
15x3asin⁡(x)(1−x2)72−15x2(x2−1)3+9xasin⁡(x)(1−x2)52+2(tan⁡2(x)+1)2cot⁡(x−1x)+4(tan⁡2(x)+1)tan⁡2(x)cot⁡(x−1x)+4(x2−1)2−6(1−x−1x)(tan⁡2(x)+1)(cot⁡2(x−1x)+1)tan⁡(x)x+6(1−x−1x)2(tan⁡2(x)+1)(cot⁡2(x−1x)+1)cot⁡(x−1x)x2+6(1−x−1x)(tan⁡2(x)+1)(cot⁡2(x−1x)+1)x2−2(1−x−1x)3(cot⁡2(x−1x)+1)2tan⁡(x)x3−4(1−x−1x)3(cot⁡2(x−1x)+1)tan⁡(x)cot⁡2(x−1x)x3−12(1−x−1x)2(cot⁡2(x−1x)+1)tan⁡(x)cot⁡(x−1x)x3−6(1−x−1x)(cot⁡2(x−1x)+1)tan⁡(x)x3\frac{15 x^{3} \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{7}{2}}} - \frac{15 x^{2}}{\left(x^{2} - 1\right)^{3}} + \frac{9 x \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + 2 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \cot{\left(\frac{x - 1}{x} \right)} + 4 \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{2}{\left(x \right)} \cot{\left(\frac{x - 1}{x} \right)} + \frac{4}{\left(x^{2} - 1\right)^{2}} - \frac{6 \left(1 - \frac{x - 1}{x}\right) \left(\tan^{2}{\left(x \right)} + 1\right) \left(\cot^{2}{\left(\frac{x - 1}{x} \right)} + 1\right) \tan{\left(x \right)}}{x} + \frac{6 \left(1 - \frac{x - 1}{x}\right)^{2} \left(\tan^{2}{\left(x \right)} + 1\right) \left(\cot^{2}{\left(\frac{x - 1}{x} \right)} + 1\right) \cot{\left(\frac{x - 1}{x} \right)}}{x^{2}} + \frac{6 \left(1 - \frac{x - 1}{x}\right) \left(\tan^{2}{\left(x \right)} + 1\right) \left(\cot^{2}{\left(\frac{x - 1}{x} \right)} + 1\right)}{x^{2}} - \frac{2 \left(1 - \frac{x - 1}{x}\right)^{3} \left(\cot^{2}{\left(\frac{x - 1}{x} \right)} + 1\right)^{2} \tan{\left(x \right)}}{x^{3}} - \frac{4 \left(1 - \frac{x - 1}{x}\right)^{3} \left(\cot^{2}{\left(\frac{x - 1}{x} \right)} + 1\right) \tan{\left(x \right)} \cot^{2}{\left(\frac{x - 1}{x} \right)}}{x^{3}} - \frac{12 \left(1 - \frac{x - 1}{x}\right)^{2} \left(\cot^{2}{\left(\frac{x - 1}{x} \right)} + 1\right) \tan{\left(x \right)} \cot{\left(\frac{x - 1}{x} \right)}}{x^{3}} - \frac{6 \left(1 - \frac{x - 1}{x}\right) \left(\cot^{2}{\left(\frac{x - 1}{x} \right)} + 1\right) \tan{\left(x \right)}}{x^{3}}
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Gráfico
Derivada de asin(x)/sqrt(1-x^2)+tan(x)*cot((x-1)/(x))
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