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x^sqrtctgx
Derivada de la función/ x^sqrtctgx

Derivada de x^sqrtctgx

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
   ________
 \/ cot(x) 
x
xcot⁡(x)x^{\sqrt{\cot{\left(x \right)}}} 
x^(sqrt(cot(x)))
Solución detallada

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

    Perola derivada

    (log⁡(cot⁡(x))+1)cot⁡cot⁡(x)2(x)\left(\log{\left(\sqrt{\cot{\left(x \right)}} \right)} + 1\right) \cot^{\frac{\sqrt{\cot{\left(x \right)}}}{2}}{\left(x \right)}

  2. Simplificamos:

    (log⁡(cot⁡(x))+2)cot⁡cot⁡(x)2(x)2\frac{\left(\log{\left(\cot{\left(x \right)} \right)} + 2\right) \cot^{\frac{\sqrt{\cot{\left(x \right)}}}{2}}{\left(x \right)}}{2}

Respuesta:

(log⁡(cot⁡(x))+2)cot⁡cot⁡(x)2(x)2\frac{\left(\log{\left(\cot{\left(x \right)} \right)} + 2\right) \cot^{\frac{\sqrt{\cot{\left(x \right)}}}{2}}{\left(x \right)}}{2}

Gráfica
02468-8-6-4-2-1010-5000050000
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Primera derivada [src] 
            /             /         2   \       \
            |             |  1   cot (x)|       |
   ________ |  ________   |- - - -------|*log(x)|
 \/ cot(x)  |\/ cot(x)    \  2      2   /       |
x          *|---------- + ----------------------|
            |    x                ________      |
            \                   \/ cot(x)       /
xcot⁡(x)((−cot⁡2(x)2−12)log⁡(x)cot⁡(x)+cot⁡(x)x)x^{\sqrt{\cot{\left(x \right)}}} \left(\frac{\left(- \frac{\cot^{2}{\left(x \right)}}{2} - \frac{1}{2}\right) \log{\left(x \right)}}{\sqrt{\cot{\left(x \right)}}} + \frac{\sqrt{\cot{\left(x \right)}}}{x}\right)
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Segunda derivada [src] 
            /                                       2                                                                                      \
            |/      ________   /       2   \       \                                                                                       |
            ||  2*\/ cot(x)    \1 + cot (x)/*log(x)|                                                                                       |
            ||- ------------ + --------------------|                                                                               2       |
   ________ ||       x                ________     |      ________                                            2       /       2   \        |
 \/ cot(x)  |\                      \/ cot(x)      /    \/ cot(x)      ________ /       2   \          1 + cot (x)    \1 + cot (x)/ *log(x)|
x          *|---------------------------------------- - ---------- + \/ cot(x) *\1 + cot (x)/*log(x) - ------------ - ---------------------|
            |                   4                            2                                             ________             3/2        |
            \                                               x                                          x*\/ cot(x)         4*cot   (x)     /
xcot⁡(x)(((cot⁡2(x)+1)log⁡(x)cot⁡(x)−2cot⁡(x)x)24−(cot⁡2(x)+1)2log⁡(x)4cot⁡32(x)+(cot⁡2(x)+1)log⁡(x)cot⁡(x)−cot⁡2(x)+1xcot⁡(x)−cot⁡(x)x2)x^{\sqrt{\cot{\left(x \right)}}} \left(\frac{\left(\frac{\left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)}}{\sqrt{\cot{\left(x \right)}}} - \frac{2 \sqrt{\cot{\left(x \right)}}}{x}\right)^{2}}{4} - \frac{\left(\cot^{2}{\left(x \right)} + 1\right)^{2} \log{\left(x \right)}}{4 \cot^{\frac{3}{2}}{\left(x \right)}} + \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \sqrt{\cot{\left(x \right)}} - \frac{\cot^{2}{\left(x \right)} + 1}{x \sqrt{\cot{\left(x \right)}}} - \frac{\sqrt{\cot{\left(x \right)}}}{x^{2}}\right)
Simplificar
Tercera derivada [src] 
            /                                         3                                                            /                            2                                                             \                                                                                                                                                       \
            |  /      ________   /       2   \       \                     /      ________   /       2   \       \ |    ________   /       2   \                                                 /       2   \|                                                                                                                                                       |
            |  |  2*\/ cot(x)    \1 + cot (x)/*log(x)|                     |  2*\/ cot(x)    \1 + cot (x)/*log(x)| |4*\/ cot(x)    \1 + cot (x)/ *log(x)       ________ /       2   \          4*\1 + cot (x)/|                                                                                                                                                       |
            |  |- ------------ + --------------------|                   3*|- ------------ + --------------------|*|------------ + --------------------- - 4*\/ cot(x) *\1 + cot (x)/*log(x) + ---------------|                2                                                                                         2                  3                         |
   ________ |  |       x                ________     |        ________     |       x                ________     | |      2                 3/2                                                      ________ |   /       2   \                                                  ________ /       2   \     /       2   \      /       2   \             /       2   \|
 \/ cot(x)  |  \                      \/ cot(x)      /    2*\/ cot(x)      \                      \/ cot(x)      / \     x               cot   (x)                                               x*\/ cot(x)  /   \1 + cot (x)/ *log(x)        3/2    /       2   \          3*\/ cot(x) *\1 + cot (x)/   3*\1 + cot (x)/    3*\1 + cot (x)/ *log(x)   3*\1 + cot (x)/|
x          *|- ---------------------------------------- + ------------ + -------------------------------------------------------------------------------------------------------------------------------------- + --------------------- - 2*cot   (x)*\1 + cot (x)/*log(x) + -------------------------- - ---------------- - ----------------------- + ---------------|
            |                     8                             3                                                                          8                                                                               ________                                                      x                        3/2                   5/2               2   ________|
            \                                                  x                                                                                                                                                       2*\/ cot(x)                                                                         4*x*cot   (x)           8*cot   (x)         2*x *\/ cot(x) /
xcot⁡(x)(−((cot⁡2(x)+1)log⁡(x)cot⁡(x)−2cot⁡(x)x)38+3((cot⁡2(x)+1)log⁡(x)cot⁡(x)−2cot⁡(x)x)((cot⁡2(x)+1)2log⁡(x)cot⁡32(x)−4(cot⁡2(x)+1)log⁡(x)cot⁡(x)+4(cot⁡2(x)+1)xcot⁡(x)+4cot⁡(x)x2)8−3(cot⁡2(x)+1)3log⁡(x)8cot⁡52(x)+(cot⁡2(x)+1)2log⁡(x)2cot⁡(x)−2(cot⁡2(x)+1)log⁡(x)cot⁡32(x)−3(cot⁡2(x)+1)24xcot⁡32(x)+3(cot⁡2(x)+1)cot⁡(x)x+3(cot⁡2(x)+1)2x2cot⁡(x)+2cot⁡(x)x3)x^{\sqrt{\cot{\left(x \right)}}} \left(- \frac{\left(\frac{\left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)}}{\sqrt{\cot{\left(x \right)}}} - \frac{2 \sqrt{\cot{\left(x \right)}}}{x}\right)^{3}}{8} + \frac{3 \left(\frac{\left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)}}{\sqrt{\cot{\left(x \right)}}} - \frac{2 \sqrt{\cot{\left(x \right)}}}{x}\right) \left(\frac{\left(\cot^{2}{\left(x \right)} + 1\right)^{2} \log{\left(x \right)}}{\cot^{\frac{3}{2}}{\left(x \right)}} - 4 \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \sqrt{\cot{\left(x \right)}} + \frac{4 \left(\cot^{2}{\left(x \right)} + 1\right)}{x \sqrt{\cot{\left(x \right)}}} + \frac{4 \sqrt{\cot{\left(x \right)}}}{x^{2}}\right)}{8} - \frac{3 \left(\cot^{2}{\left(x \right)} + 1\right)^{3} \log{\left(x \right)}}{8 \cot^{\frac{5}{2}}{\left(x \right)}} + \frac{\left(\cot^{2}{\left(x \right)} + 1\right)^{2} \log{\left(x \right)}}{2 \sqrt{\cot{\left(x \right)}}} - 2 \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \cot^{\frac{3}{2}}{\left(x \right)} - \frac{3 \left(\cot^{2}{\left(x \right)} + 1\right)^{2}}{4 x \cot^{\frac{3}{2}}{\left(x \right)}} + \frac{3 \left(\cot^{2}{\left(x \right)} + 1\right) \sqrt{\cot{\left(x \right)}}}{x} + \frac{3 \left(\cot^{2}{\left(x \right)} + 1\right)}{2 x^{2} \sqrt{\cot{\left(x \right)}}} + \frac{2 \sqrt{\cot{\left(x \right)}}}{x^{3}}\right)
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Gráfico
Derivada de x^sqrtctgx
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