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y=(tglnx)^arcsinx
Derivada de la función/ tglnx/ arcsin/ y=(tglnx)^arcsinx

Derivada de y=(tglnx)^arcsinx

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

Gráfico:

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Solución

Ha introducido [src] 
   asin(x)        
tan       (log(x))
tan⁡asin⁡(x)(log⁡(x))\tan^{\operatorname{asin}{\left(x \right)}}{\left(\log{\left(x \right)} \right)} 
tan(log(x))^asin(x)
Solución detallada

  1. No logro encontrar los pasos en la búsqueda de esta derivada.

    Perola derivada

    (log⁡(asin⁡(x))+1)asin⁡asin⁡(x)(x)\left(\log{\left(\operatorname{asin}{\left(x \right)} \right)} + 1\right) \operatorname{asin}^{\operatorname{asin}{\left(x \right)}}{\left(x \right)}

Respuesta:

(log⁡(asin⁡(x))+1)asin⁡asin⁡(x)(x)\left(\log{\left(\operatorname{asin}{\left(x \right)} \right)} + 1\right) \operatorname{asin}^{\operatorname{asin}{\left(x \right)}}{\left(x \right)}

Gráfica
02468-8-6-4-2-101003
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
                   /                   /       2        \        \
   asin(x)         |log(tan(log(x)))   \1 + tan (log(x))/*asin(x)|
tan       (log(x))*|---------------- + --------------------------|
                   |     ________            x*tan(log(x))       |
                   |    /      2                                 |
                   \  \/  1 - x                                  /
(log⁡(tan⁡(log⁡(x)))1−x2+(tan⁡2(log⁡(x))+1)asin⁡(x)xtan⁡(log⁡(x)))tan⁡asin⁡(x)(log⁡(x))\left(\frac{\log{\left(\tan{\left(\log{\left(x \right)} \right)} \right)}}{\sqrt{1 - x^{2}}} + \frac{\left(\tan^{2}{\left(\log{\left(x \right)} \right)} + 1\right) \operatorname{asin}{\left(x \right)}}{x \tan{\left(\log{\left(x \right)} \right)}}\right) \tan^{\operatorname{asin}{\left(x \right)}}{\left(\log{\left(x \right)} \right)}
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Segunda derivada [src] 
                   /                                               2                                                                         2                                                                 \
                   |/                   /       2        \        \                           /       2        \           /       2        \            /       2        \                /       2        \  |
   asin(x)         ||log(tan(log(x)))   \1 + tan (log(x))/*asin(x)|    x*log(tan(log(x)))   2*\1 + tan (log(x))/*asin(x)   \1 + tan (log(x))/ *asin(x)   \1 + tan (log(x))/*asin(x)      2*\1 + tan (log(x))/  |
tan       (log(x))*||---------------- + --------------------------|  + ------------------ + ---------------------------- - --------------------------- - -------------------------- + -------------------------|
                   ||     ________            x*tan(log(x))       |               3/2                     2                       2    2                        2                          ________            |
                   ||    /      2                                 |       /     2\                       x                       x *tan (log(x))               x *tan(log(x))             /      2             |
                   \\  \/  1 - x                                  /       \1 - x /                                                                                                    x*\/  1 - x  *tan(log(x))/
(xlog⁡(tan⁡(log⁡(x)))(1−x2)32+(log⁡(tan⁡(log⁡(x)))1−x2+(tan⁡2(log⁡(x))+1)asin⁡(x)xtan⁡(log⁡(x)))2+2(tan⁡2(log⁡(x))+1)x1−x2tan⁡(log⁡(x))−(tan⁡2(log⁡(x))+1)2asin⁡(x)x2tan⁡2(log⁡(x))+2(tan⁡2(log⁡(x))+1)asin⁡(x)x2−(tan⁡2(log⁡(x))+1)asin⁡(x)x2tan⁡(log⁡(x)))tan⁡asin⁡(x)(log⁡(x))\left(\frac{x \log{\left(\tan{\left(\log{\left(x \right)} \right)} \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \left(\frac{\log{\left(\tan{\left(\log{\left(x \right)} \right)} \right)}}{\sqrt{1 - x^{2}}} + \frac{\left(\tan^{2}{\left(\log{\left(x \right)} \right)} + 1\right) \operatorname{asin}{\left(x \right)}}{x \tan{\left(\log{\left(x \right)} \right)}}\right)^{2} + \frac{2 \left(\tan^{2}{\left(\log{\left(x \right)} \right)} + 1\right)}{x \sqrt{1 - x^{2}} \tan{\left(\log{\left(x \right)} \right)}} - \frac{\left(\tan^{2}{\left(\log{\left(x \right)} \right)} + 1\right)^{2} \operatorname{asin}{\left(x \right)}}{x^{2} \tan^{2}{\left(\log{\left(x \right)} \right)}} + \frac{2 \left(\tan^{2}{\left(\log{\left(x \right)} \right)} + 1\right) \operatorname{asin}{\left(x \right)}}{x^{2}} - \frac{\left(\tan^{2}{\left(\log{\left(x \right)} \right)} + 1\right) \operatorname{asin}{\left(x \right)}}{x^{2} \tan{\left(\log{\left(x \right)} \right)}}\right) \tan^{\operatorname{asin}{\left(x \right)}}{\left(\log{\left(x \right)} \right)}
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Tercera derivada [src] 
                   /                                               3                                                                        /                                                                      2                                                                 \                                                                                                                               2                                  2                                                       3                                                              2                                                   \
                   |/                   /       2        \        \                         /                   /       2        \        \ |                       /       2        \           /       2        \            /       2        \                /       2        \  |     /       2        \              2                        /       2        \      /       2        \     /       2        \                 /       2        \            /       2        \        /       2        \              /       2        \             /       2        \              /       2        \                    |
   asin(x)         ||log(tan(log(x)))   \1 + tan (log(x))/*asin(x)|    log(tan(log(x)))     |log(tan(log(x)))   \1 + tan (log(x))/*asin(x)| |x*log(tan(log(x)))   2*\1 + tan (log(x))/*asin(x)   \1 + tan (log(x))/ *asin(x)   \1 + tan (log(x))/*asin(x)      2*\1 + tan (log(x))/  |   6*\1 + tan (log(x))/*asin(x)   3*x *log(tan(log(x)))     3*\1 + tan (log(x))/    6*\1 + tan (log(x))/   4*\1 + tan (log(x))/ *asin(x)      3*\1 + tan (log(x))/          3*\1 + tan (log(x))/      2*\1 + tan (log(x))/ *asin(x)   2*\1 + tan (log(x))/*asin(x)   3*\1 + tan (log(x))/ *asin(x)   4*\1 + tan (log(x))/*asin(x)*tan(log(x))|
tan       (log(x))*||---------------- + --------------------------|  + ---------------- + 3*|---------------- + --------------------------|*|------------------ + ---------------------------- - --------------------------- - -------------------------- + -------------------------| - ---------------------------- + --------------------- + ----------------------- + -------------------- - ----------------------------- - --------------------------- - -------------------------- + ----------------------------- + ---------------------------- + ----------------------------- + ----------------------------------------|
                   ||     ________            x*tan(log(x))       |              3/2        |     ________            x*tan(log(x))       | |           3/2                     2                       2    2                        2                          ________            |                 3                             5/2                3/2                        ________               3                            ________                      ________                       3    3                          3                              3    2                                      3                   |
                   ||    /      2                                 |      /     2\           |    /      2                                 | |   /     2\                       x                       x *tan (log(x))               x *tan(log(x))             /      2             |                x                      /     2\           /     2\                      2   /      2               x *tan(log(x))           2   /      2     2            2   /      2                       x *tan (log(x))                 x *tan(log(x))                 x *tan (log(x))                             x                    |
                   \\  \/  1 - x                                  /      \1 - x /           \  \/  1 - x                                  / \   \1 - x /                                                                                                    x*\/  1 - x  *tan(log(x))/                                       \1 - x /           \1 - x /   *tan(log(x))      x *\/  1 - x                                        x *\/  1 - x  *tan (log(x))   x *\/  1 - x  *tan(log(x))                                                                                                                                          /
(3x2log⁡(tan⁡(log⁡(x)))(1−x2)52+(log⁡(tan⁡(log⁡(x)))1−x2+(tan⁡2(log⁡(x))+1)asin⁡(x)xtan⁡(log⁡(x)))3+3(log⁡(tan⁡(log⁡(x)))1−x2+(tan⁡2(log⁡(x))+1)asin⁡(x)xtan⁡(log⁡(x)))(xlog⁡(tan⁡(log⁡(x)))(1−x2)32+2(tan⁡2(log⁡(x))+1)x1−x2tan⁡(log⁡(x))−(tan⁡2(log⁡(x))+1)2asin⁡(x)x2tan⁡2(log⁡(x))+2(tan⁡2(log⁡(x))+1)asin⁡(x)x2−(tan⁡2(log⁡(x))+1)asin⁡(x)x2tan⁡(log⁡(x)))+3(tan⁡2(log⁡(x))+1)(1−x2)32tan⁡(log⁡(x))+log⁡(tan⁡(log⁡(x)))(1−x2)32−3(tan⁡2(log⁡(x))+1)2x21−x2tan⁡2(log⁡(x))+6(tan⁡2(log⁡(x))+1)x21−x2−3(tan⁡2(log⁡(x))+1)x21−x2tan⁡(log⁡(x))+2(tan⁡2(log⁡(x))+1)3asin⁡(x)x3tan⁡3(log⁡(x))−4(tan⁡2(log⁡(x))+1)2asin⁡(x)x3tan⁡(log⁡(x))+3(tan⁡2(log⁡(x))+1)2asin⁡(x)x3tan⁡2(log⁡(x))+4(tan⁡2(log⁡(x))+1)tan⁡(log⁡(x))asin⁡(x)x3−6(tan⁡2(log⁡(x))+1)asin⁡(x)x3+2(tan⁡2(log⁡(x))+1)asin⁡(x)x3tan⁡(log⁡(x)))tan⁡asin⁡(x)(log⁡(x))\left(\frac{3 x^{2} \log{\left(\tan{\left(\log{\left(x \right)} \right)} \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \left(\frac{\log{\left(\tan{\left(\log{\left(x \right)} \right)} \right)}}{\sqrt{1 - x^{2}}} + \frac{\left(\tan^{2}{\left(\log{\left(x \right)} \right)} + 1\right) \operatorname{asin}{\left(x \right)}}{x \tan{\left(\log{\left(x \right)} \right)}}\right)^{3} + 3 \left(\frac{\log{\left(\tan{\left(\log{\left(x \right)} \right)} \right)}}{\sqrt{1 - x^{2}}} + \frac{\left(\tan^{2}{\left(\log{\left(x \right)} \right)} + 1\right) \operatorname{asin}{\left(x \right)}}{x \tan{\left(\log{\left(x \right)} \right)}}\right) \left(\frac{x \log{\left(\tan{\left(\log{\left(x \right)} \right)} \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{2 \left(\tan^{2}{\left(\log{\left(x \right)} \right)} + 1\right)}{x \sqrt{1 - x^{2}} \tan{\left(\log{\left(x \right)} \right)}} - \frac{\left(\tan^{2}{\left(\log{\left(x \right)} \right)} + 1\right)^{2} \operatorname{asin}{\left(x \right)}}{x^{2} \tan^{2}{\left(\log{\left(x \right)} \right)}} + \frac{2 \left(\tan^{2}{\left(\log{\left(x \right)} \right)} + 1\right) \operatorname{asin}{\left(x \right)}}{x^{2}} - \frac{\left(\tan^{2}{\left(\log{\left(x \right)} \right)} + 1\right) \operatorname{asin}{\left(x \right)}}{x^{2} \tan{\left(\log{\left(x \right)} \right)}}\right) + \frac{3 \left(\tan^{2}{\left(\log{\left(x \right)} \right)} + 1\right)}{\left(1 - x^{2}\right)^{\frac{3}{2}} \tan{\left(\log{\left(x \right)} \right)}} + \frac{\log{\left(\tan{\left(\log{\left(x \right)} \right)} \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{3 \left(\tan^{2}{\left(\log{\left(x \right)} \right)} + 1\right)^{2}}{x^{2} \sqrt{1 - x^{2}} \tan^{2}{\left(\log{\left(x \right)} \right)}} + \frac{6 \left(\tan^{2}{\left(\log{\left(x \right)} \right)} + 1\right)}{x^{2} \sqrt{1 - x^{2}}} - \frac{3 \left(\tan^{2}{\left(\log{\left(x \right)} \right)} + 1\right)}{x^{2} \sqrt{1 - x^{2}} \tan{\left(\log{\left(x \right)} \right)}} + \frac{2 \left(\tan^{2}{\left(\log{\left(x \right)} \right)} + 1\right)^{3} \operatorname{asin}{\left(x \right)}}{x^{3} \tan^{3}{\left(\log{\left(x \right)} \right)}} - \frac{4 \left(\tan^{2}{\left(\log{\left(x \right)} \right)} + 1\right)^{2} \operatorname{asin}{\left(x \right)}}{x^{3} \tan{\left(\log{\left(x \right)} \right)}} + \frac{3 \left(\tan^{2}{\left(\log{\left(x \right)} \right)} + 1\right)^{2} \operatorname{asin}{\left(x \right)}}{x^{3} \tan^{2}{\left(\log{\left(x \right)} \right)}} + \frac{4 \left(\tan^{2}{\left(\log{\left(x \right)} \right)} + 1\right) \tan{\left(\log{\left(x \right)} \right)} \operatorname{asin}{\left(x \right)}}{x^{3}} - \frac{6 \left(\tan^{2}{\left(\log{\left(x \right)} \right)} + 1\right) \operatorname{asin}{\left(x \right)}}{x^{3}} + \frac{2 \left(\tan^{2}{\left(\log{\left(x \right)} \right)} + 1\right) \operatorname{asin}{\left(x \right)}}{x^{3} \tan{\left(\log{\left(x \right)} \right)}}\right) \tan^{\operatorname{asin}{\left(x \right)}}{\left(\log{\left(x \right)} \right)}
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Gráfico
Derivada de y=(tglnx)^arcsinx
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