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(x^x)+(x^(arccosx))

Derivada de (x^x)+(x^(arccosx))

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

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Solución

Solución detallada
  1. diferenciamos xx+xacos(x)x^{x} + x^{\operatorname{acos}{\left(x \right)}} miembro por miembro:

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

      Perola derivada

      xx(log(x)+1)x^{x} \left(\log{\left(x \right)} + 1\right)

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

      Perola derivada

      (log(acos(x))+1)acosacos(x)(x)\left(\log{\left(\operatorname{acos}{\left(x \right)} \right)} + 1\right) \operatorname{acos}^{\operatorname{acos}{\left(x \right)}}{\left(x \right)}

    Como resultado de: xx(log(x)+1)+(log(acos(x))+1)acosacos(x)(x)x^{x} \left(\log{\left(x \right)} + 1\right) + \left(\log{\left(\operatorname{acos}{\left(x \right)} \right)} + 1\right) \operatorname{acos}^{\operatorname{acos}{\left(x \right)}}{\left(x \right)}


Respuesta:

xx(log(x)+1)+(log(acos(x))+1)acosacos(x)(x)x^{x} \left(\log{\left(x \right)} + 1\right) + \left(\log{\left(\operatorname{acos}{\left(x \right)} \right)} + 1\right) \operatorname{acos}^{\operatorname{acos}{\left(x \right)}}{\left(x \right)}

Gráfica
02468-8-6-4-2-1010-5000000000050000000000
Primera derivada [src]
 x                 acos(x) /acos(x)      log(x)  \
x *(1 + log(x)) + x       *|------- - -----------|
                           |   x         ________|
                           |            /      2 |
                           \          \/  1 - x  /
xx(log(x)+1)+xacos(x)(log(x)1x2+acos(x)x)x^{x} \left(\log{\left(x \right)} + 1\right) + x^{\operatorname{acos}{\left(x \right)}} \left(- \frac{\log{\left(x \right)}}{\sqrt{1 - x^{2}}} + \frac{\operatorname{acos}{\left(x \right)}}{x}\right)
Segunda derivada [src]
 x                                                      2                                                   
x     x             2    acos(x) /   log(x)     acos(x)\     acos(x) /acos(x)         2           x*log(x) \
-- + x *(1 + log(x))  + x       *|----------- - -------|  - x       *|------- + ------------- + -----------|
x                                |   ________      x   |             |    2          ________           3/2|
                                 |  /      2           |             |   x          /      2    /     2\   |
                                 \\/  1 - x            /             \          x*\/  1 - x     \1 - x /   /
xx(log(x)+1)2+xacos(x)(log(x)1x2acos(x)x)2xacos(x)(xlog(x)(1x2)32+2x1x2+acos(x)x2)+xxxx^{x} \left(\log{\left(x \right)} + 1\right)^{2} + x^{\operatorname{acos}{\left(x \right)}} \left(\frac{\log{\left(x \right)}}{\sqrt{1 - x^{2}}} - \frac{\operatorname{acos}{\left(x \right)}}{x}\right)^{2} - x^{\operatorname{acos}{\left(x \right)}} \left(\frac{x \log{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{2}{x \sqrt{1 - x^{2}}} + \frac{\operatorname{acos}{\left(x \right)}}{x^{2}}\right) + \frac{x^{x}}{x}
Tercera derivada [src]
                    x                                   3            /                                                            2       \      x                                                                                          
 x             3   x     acos(x) /   log(x)     acos(x)\     acos(x) |     3           log(x)           3          2*acos(x)   3*x *log(x)|   3*x *(1 + log(x))      acos(x) /   log(x)     acos(x)\ /acos(x)         2           x*log(x) \
x *(1 + log(x))  - -- - x       *|----------- - -------|  - x       *|----------- + ----------- - -------------- - --------- + -----------| + ----------------- + 3*x       *|----------- - -------|*|------- + ------------- + -----------|
                    2            |   ________      x   |             |        3/2           3/2         ________        3              5/2|           x                      |   ________      x   | |    2          ________           3/2|
                   x             |  /      2           |             |/     2\      /     2\       2   /      2        x       /     2\   |                                  |  /      2           | |   x          /      2    /     2\   |
                                 \\/  1 - x            /             \\1 - x /      \1 - x /      x *\/  1 - x                 \1 - x /   /                                  \\/  1 - x            / \          x*\/  1 - x     \1 - x /   /
xx(log(x)+1)3xacos(x)(log(x)1x2acos(x)x)3+3xacos(x)(log(x)1x2acos(x)x)(xlog(x)(1x2)32+2x1x2+acos(x)x2)xacos(x)(3x2log(x)(1x2)52+log(x)(1x2)32+3(1x2)323x21x22acos(x)x3)+3xx(log(x)+1)xxxx2x^{x} \left(\log{\left(x \right)} + 1\right)^{3} - x^{\operatorname{acos}{\left(x \right)}} \left(\frac{\log{\left(x \right)}}{\sqrt{1 - x^{2}}} - \frac{\operatorname{acos}{\left(x \right)}}{x}\right)^{3} + 3 x^{\operatorname{acos}{\left(x \right)}} \left(\frac{\log{\left(x \right)}}{\sqrt{1 - x^{2}}} - \frac{\operatorname{acos}{\left(x \right)}}{x}\right) \left(\frac{x \log{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{2}{x \sqrt{1 - x^{2}}} + \frac{\operatorname{acos}{\left(x \right)}}{x^{2}}\right) - x^{\operatorname{acos}{\left(x \right)}} \left(\frac{3 x^{2} \log{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{\log{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{3}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{3}{x^{2} \sqrt{1 - x^{2}}} - \frac{2 \operatorname{acos}{\left(x \right)}}{x^{3}}\right) + \frac{3 x^{x} \left(\log{\left(x \right)} + 1\right)}{x} - \frac{x^{x}}{x^{2}}
Gráfico
Derivada de (x^x)+(x^(arccosx))