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y=arcsin^2tglnx
Derivada de la función/ tglnx/ sin^2/ arcsin/ y=arcsin^2tglnx

Derivada de y=arcsin^2tglnx

Función f() - derivada -er orden en el punto
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Gráfico:

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Solución

Ha introducido [src] 
    2                 
asin (x)*tan(x)*log(x)
tan⁡(x)asin⁡2(x)log⁡(x)\tan{\left(x \right)} \operatorname{asin}^{2}{\left(x \right)} \log{\left(x \right)} 
(asin(x)^2*tan(x))*log(x)
Gráfica
02468-8-6-4-2-10101-1
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Trazar el gráfico f'(x)
Primera derivada [src] 
                                                         2          
/    2    /       2   \   2*asin(x)*tan(x)\          asin (x)*tan(x)
|asin (x)*\1 + tan (x)/ + ----------------|*log(x) + ---------------
|                              ________   |                 x       
|                             /      2    |                         
\                           \/  1 - x     /
((tan⁡2(x)+1)asin⁡2(x)+2tan⁡(x)asin⁡(x)1−x2)log⁡(x)+tan⁡(x)asin⁡2(x)x\left(\left(\tan^{2}{\left(x \right)} + 1\right) \operatorname{asin}^{2}{\left(x \right)} + \frac{2 \tan{\left(x \right)} \operatorname{asin}{\left(x \right)}}{\sqrt{1 - x^{2}}}\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)} \operatorname{asin}^{2}{\left(x \right)}}{x}
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Segunda derivada [src] 
                                                                                                                            //       2   \             2*tan(x) \        
                                                                                                                          2*|\1 + tan (x)/*asin(x) + -----------|*asin(x)
                                                                                                                            |                           ________|        
  /                                                                     /       2   \        \              2               |                          /      2 |        
  |/     1       x*asin(x) \              2    /       2   \          2*\1 + tan (x)/*asin(x)|          asin (x)*tan(x)     \                        \/  1 - x  /        
2*||- ------- + -----------|*tan(x) + asin (x)*\1 + tan (x)/*tan(x) + -----------------------|*log(x) - --------------- + -----------------------------------------------
  ||        2           3/2|                                                   ________      |                  2                                x                       
  ||  -1 + x    /     2\   |                                                  /      2       |                 x                                                         
  \\            \1 - x /   /                                                \/  1 - x        /
2((xasin⁡(x)(1−x2)32−1x2−1)tan⁡(x)+(tan⁡2(x)+1)tan⁡(x)asin⁡2(x)+2(tan⁡2(x)+1)asin⁡(x)1−x2)log⁡(x)+2((tan⁡2(x)+1)asin⁡(x)+2tan⁡(x)1−x2)asin⁡(x)x−tan⁡(x)asin⁡2(x)x22 \left(\left(\frac{x \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{1}{x^{2} - 1}\right) \tan{\left(x \right)} + \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} \operatorname{asin}^{2}{\left(x \right)} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right) \operatorname{asin}{\left(x \right)}}{\sqrt{1 - x^{2}}}\right) \log{\left(x \right)} + \frac{2 \left(\left(\tan^{2}{\left(x \right)} + 1\right) \operatorname{asin}{\left(x \right)} + \frac{2 \tan{\left(x \right)}}{\sqrt{1 - x^{2}}}\right) \operatorname{asin}{\left(x \right)}}{x} - \frac{\tan{\left(x \right)} \operatorname{asin}^{2}{\left(x \right)}}{x^{2}}
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Tercera derivada [src] 
                                                                                                                                                                                      /                                                                     /       2   \        \                                                                      
                                                                                                                                                                                      |/     1       x*asin(x) \              2    /       2   \          2*\1 + tan (x)/*asin(x)|     //       2   \             2*tan(x) \                            
                                                                                                                                                                                    6*||- ------- + -----------|*tan(x) + asin (x)*\1 + tan (x)/*tan(x) + -----------------------|   3*|\1 + tan (x)/*asin(x) + -----------|*asin(x)                    
                                                                                                                                                                                      ||        2           3/2|                                                   ________      |     |                           ________|                            
  //                              2        \                                                                                                 /       2   \               \            ||  -1 + x    /     2\   |                                                  /      2       |     |                          /      2 |                 2          
  ||  asin(x)        3*x       3*x *asin(x)|            /       2   \ /     1       x*asin(x) \       2    /       2   \ /         2   \   6*\1 + tan (x)/*asin(x)*tan(x)|            \\            \1 - x /   /                                                \/  1 - x        /     \                        \/  1 - x  /           2*asin (x)*tan(x)
2*||----------- + ---------- + ------------|*tan(x) + 3*\1 + tan (x)/*|- ------- + -----------| + asin (x)*\1 + tan (x)/*\1 + 3*tan (x)/ + ------------------------------|*log(x) + ---------------------------------------------------------------------------------------------- - ----------------------------------------------- + -----------------
  ||        3/2            2           5/2 |                          |        2           3/2|                                                        ________          |                                                        x                                                                          2                                  3       
  ||/     2\      /      2\    /     2\    |                          |  -1 + x    /     2\   |                                                       /      2           |                                                                                                                                  x                                  x        
  \\\1 - x /      \-1 + x /    \1 - x /    /                          \            \1 - x /   /                                                     \/  1 - x            /
2(3(xasin⁡(x)(1−x2)32−1x2−1)(tan⁡2(x)+1)+(tan⁡2(x)+1)(3tan⁡2(x)+1)asin⁡2(x)+(3x2asin⁡(x)(1−x2)52+3x(x2−1)2+asin⁡(x)(1−x2)32)tan⁡(x)+6(tan⁡2(x)+1)tan⁡(x)asin⁡(x)1−x2)log⁡(x)+6((xasin⁡(x)(1−x2)32−1x2−1)tan⁡(x)+(tan⁡2(x)+1)tan⁡(x)asin⁡2(x)+2(tan⁡2(x)+1)asin⁡(x)1−x2)x−3((tan⁡2(x)+1)asin⁡(x)+2tan⁡(x)1−x2)asin⁡(x)x2+2tan⁡(x)asin⁡2(x)x32 \left(3 \left(\frac{x \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{1}{x^{2} - 1}\right) \left(\tan^{2}{\left(x \right)} + 1\right) + \left(\tan^{2}{\left(x \right)} + 1\right) \left(3 \tan^{2}{\left(x \right)} + 1\right) \operatorname{asin}^{2}{\left(x \right)} + \left(\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}} + \frac{\operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}}\right) \tan{\left(x \right)} + \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} \operatorname{asin}{\left(x \right)}}{\sqrt{1 - x^{2}}}\right) \log{\left(x \right)} + \frac{6 \left(\left(\frac{x \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{1}{x^{2} - 1}\right) \tan{\left(x \right)} + \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} \operatorname{asin}^{2}{\left(x \right)} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right) \operatorname{asin}{\left(x \right)}}{\sqrt{1 - x^{2}}}\right)}{x} - \frac{3 \left(\left(\tan^{2}{\left(x \right)} + 1\right) \operatorname{asin}{\left(x \right)} + \frac{2 \tan{\left(x \right)}}{\sqrt{1 - x^{2}}}\right) \operatorname{asin}{\left(x \right)}}{x^{2}} + \frac{2 \tan{\left(x \right)} \operatorname{asin}^{2}{\left(x \right)}}{x^{3}}
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Gráfico
Derivada de y=arcsin^2tglnx
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