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е^arcsin(√1-x)arctglnx
Derivada de la función/ tglnx/ arctg/ arcsin/ е^arcsin(√1-x)arctglnx

Derivada de е^arcsin(√1-x)arctglnx

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

Gráfico:

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Solución

Ha introducido [src] 
     /  ___    \             
 asin\\/ 1  - x/             
E               *atan(log(x))
easin⁡(−x+1)atan⁡(log⁡(x))e^{\operatorname{asin}{\left(- x + \sqrt{1} \right)}} \operatorname{atan}{\left(\log{\left(x \right)} \right)} 
E^asin(sqrt(1) - x)*atan(log(x))
Gráfica
02468-8-6-4-2-1010-2020
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Trazar el gráfico f'(x)
Primera derivada [src] 
     /  ___    \                     /  ___    \
 asin\\/ 1  - x/                 asin\\/ 1  - x/
e                  atan(log(x))*e               
---------------- - -----------------------------
  /       2   \            __________________   
x*\1 + log (x)/           /                2    
                         /      /  ___    \     
                       \/   1 - \\/ 1  - x/
−easin⁡(−x+1)atan⁡(log⁡(x))1−(−x+1)2+easin⁡(−x+1)x(log⁡(x)2+1)- \frac{e^{\operatorname{asin}{\left(- x + \sqrt{1} \right)}} \operatorname{atan}{\left(\log{\left(x \right)} \right)}}{\sqrt{1 - \left(- x + \sqrt{1}\right)^{2}}} + \frac{e^{\operatorname{asin}{\left(- x + \sqrt{1} \right)}}}{x \left(\log{\left(x \right)}^{2} + 1\right)}
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Segunda derivada [src] 
 /                                                          2*log(x)                                      \               
 |                                                    1 + -----------                                     |               
 |                                                               2                                        |               
 |/      1                -1 + x     \                    1 + log (x)                    2                |  -asin(-1 + x)
-||-------------- + -----------------|*atan(log(x)) + ---------------- + ---------------------------------|*e             
 ||             2                 3/2|                 2 /       2   \                      ______________|               
 ||-1 + (-1 + x)    /           2\   |                x *\1 + log (x)/     /       2   \   /            2 |               
 \\                 \1 - (1 - x) /   /                                   x*\1 + log (x)/*\/  1 - (1 - x)  /
−((1(x−1)2−1+x−1(1−(1−x)2)32)atan⁡(log⁡(x))+2x1−(1−x)2(log⁡(x)2+1)+1+2log⁡(x)log⁡(x)2+1x2(log⁡(x)2+1))e−asin⁡(x−1)- \left(\left(\frac{1}{\left(x - 1\right)^{2} - 1} + \frac{x - 1}{\left(1 - \left(1 - x\right)^{2}\right)^{\frac{3}{2}}}\right) \operatorname{atan}{\left(\log{\left(x \right)} \right)} + \frac{2}{x \sqrt{1 - \left(1 - x\right)^{2}} \left(\log{\left(x \right)}^{2} + 1\right)} + \frac{1 + \frac{2 \log{\left(x \right)}}{\log{\left(x \right)}^{2} + 1}}{x^{2} \left(\log{\left(x \right)}^{2} + 1\right)}\right) e^{- \operatorname{asin}{\left(x - 1 \right)}}
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Tercera derivada [src] 
/                                                                                                                        /                                       2      \                                     \               
|                                                                               /      1                -1 + x     \     |         1          3*log(x)      4*log (x)   |                                     |               
|                                                                             3*|-------------- + -----------------|   2*|1 - ----------- + ----------- + --------------|            /      2*log(x) \        |               
|                                                                               |             2                 3/2|     |           2             2                   2|          3*|1 + -----------|        |               
|  /                                                     2   \                  |-1 + (-1 + x)    /           2\   |     |    1 + log (x)   1 + log (x)   /       2   \ |            |           2   |        |               
|  |        2               3*(-1 + x)         3*(-1 + x)    |                  \                 \1 - (1 - x) /   /     \                                \1 + log (x)/ /            \    1 + log (x)/        |  -asin(-1 + x)
|- |----------------- - ----------------- + -----------------|*atan(log(x)) - -------------------------------------- + -------------------------------------------------- + ----------------------------------|*e             
|  |              3/2                   2                 5/2|                             /       2   \                                 3 /       2   \                                        ______________|               
|  |/           2\      /             2\    /           2\   |                           x*\1 + log (x)/                                x *\1 + log (x)/                     2 /       2   \   /            2 |               
\  \\1 - (1 - x) /      \-1 + (-1 + x) /    \1 - (1 - x) /   /                                                                                                              x *\1 + log (x)/*\/  1 - (1 - x)  /
(−(−3(x−1)((x−1)2−1)2+2(1−(1−x)2)32+3(x−1)2(1−(1−x)2)52)atan⁡(log⁡(x))−3(1(x−1)2−1+x−1(1−(1−x)2)32)x(log⁡(x)2+1)+3(1+2log⁡(x)log⁡(x)2+1)x21−(1−x)2(log⁡(x)2+1)+2(1+3log⁡(x)log⁡(x)2+1−1log⁡(x)2+1+4log⁡(x)2(log⁡(x)2+1)2)x3(log⁡(x)2+1))e−asin⁡(x−1)\left(- \left(- \frac{3 \left(x - 1\right)}{\left(\left(x - 1\right)^{2} - 1\right)^{2}} + \frac{2}{\left(1 - \left(1 - x\right)^{2}\right)^{\frac{3}{2}}} + \frac{3 \left(x - 1\right)^{2}}{\left(1 - \left(1 - x\right)^{2}\right)^{\frac{5}{2}}}\right) \operatorname{atan}{\left(\log{\left(x \right)} \right)} - \frac{3 \left(\frac{1}{\left(x - 1\right)^{2} - 1} + \frac{x - 1}{\left(1 - \left(1 - x\right)^{2}\right)^{\frac{3}{2}}}\right)}{x \left(\log{\left(x \right)}^{2} + 1\right)} + \frac{3 \left(1 + \frac{2 \log{\left(x \right)}}{\log{\left(x \right)}^{2} + 1}\right)}{x^{2} \sqrt{1 - \left(1 - x\right)^{2}} \left(\log{\left(x \right)}^{2} + 1\right)} + \frac{2 \left(1 + \frac{3 \log{\left(x \right)}}{\log{\left(x \right)}^{2} + 1} - \frac{1}{\log{\left(x \right)}^{2} + 1} + \frac{4 \log{\left(x \right)}^{2}}{\left(\log{\left(x \right)}^{2} + 1\right)^{2}}\right)}{x^{3} \left(\log{\left(x \right)}^{2} + 1\right)}\right) e^{- \operatorname{asin}{\left(x - 1 \right)}}
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Gráfico
Derivada de е^arcsin(√1-x)arctglnx
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