Derivada de y=x^arctg(sqrt(x))

Ha introducido [src]

     /  ___\
 atan\\/ x /
x

x^{\operatorname{atan}{\left(\sqrt{x} \right)}}

x^atan(sqrt(x))

Solución detallada

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Perola derivada

$\left(\log{\left(\operatorname{atan}{\left(\sqrt{x} \right)} \right)} + 1\right) \operatorname{atan}^{\operatorname{atan}{\left(\sqrt{x} \right)}}{\left(\sqrt{x} \right)}$

Respuesta:

$\left(\log{\left(\operatorname{atan}{\left(\sqrt{x} \right)} \right)} + 1\right) \operatorname{atan}^{\operatorname{atan}{\left(\sqrt{x} \right)}}{\left(\sqrt{x} \right)}$

Gráfica

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Primera derivada [src]

     /  ___\ /    /  ___\                  \
 atan\\/ x / |atan\\/ x /        log(x)    |
x           *|----------- + ---------------|
             |     x            ___        |
             \              2*\/ x *(1 + x)/

x^{\operatorname{atan}{\left(\sqrt{x} \right)}} \left(\frac{\operatorname{atan}{\left(\sqrt{x} \right)}}{x} + \frac{\log{\left(x \right)}}{2 \sqrt{x} \left(x + 1\right)}\right)

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Segunda derivada [src]

             /                               2                                                                 \
             |/      /  ___\                \                                                                  |
             ||2*atan\\/ x /       log(x)   |                                                                  |
             ||------------- + -------------|                                                                  |
     /  ___\ ||      x           ___        |                       /  ___\                                    |
 atan\\/ x / |\                \/ x *(1 + x)/         1         atan\\/ x /        log(x)            log(x)    |
x           *|-------------------------------- + ------------ - ----------- - ---------------- - --------------|
             |               4                    3/2                 2           ___        2      3/2        |
             \                                   x   *(1 + x)        x        2*\/ x *(1 + x)    4*x   *(1 + x)/

x^{\operatorname{atan}{\left(\sqrt{x} \right)}} \left(\frac{\left(\frac{2 \operatorname{atan}{\left(\sqrt{x} \right)}}{x} + \frac{\log{\left(x \right)}}{\sqrt{x} \left(x + 1\right)}\right)^{2}}{4} - \frac{\operatorname{atan}{\left(\sqrt{x} \right)}}{x^{2}} - \frac{\log{\left(x \right)}}{2 \sqrt{x} \left(x + 1\right)^{2}} - \frac{\log{\left(x \right)}}{4 x^{\frac{3}{2}} \left(x + 1\right)} + \frac{1}{x^{\frac{3}{2}} \left(x + 1\right)}\right)

Simplificar

Tercera derivada [src]

             /                               3                                                                                                                                                                                                            \
             |/      /  ___\                \                                                         /      /  ___\                \ /                       /  ___\                                \                                                    |
             ||2*atan\\/ x /       log(x)   |                                                         |2*atan\\/ x /       log(x)   | |       4         4*atan\\/ x /      log(x)         2*log(x)   |                                                    |
             ||------------- + -------------|                                                       3*|------------- + -------------|*|- ------------ + ------------- + ------------ + --------------|                                                    |
     /  ___\ ||      x           ___        |          /  ___\                                        |      x           ___        | |   3/2                  2         3/2             ___        2|                                                    |
 atan\\/ x / |\                \/ x *(1 + x)/    2*atan\\/ x /         9                 3            \                \/ x *(1 + x)/ \  x   *(1 + x)         x         x   *(1 + x)   \/ x *(1 + x) /       log(x)            log(x)          3*log(x)   |
x           *|-------------------------------- + ------------- - -------------- - --------------- - -------------------------------------------------------------------------------------------------- + -------------- + --------------- + --------------|
             |               8                          3           5/2              3/2        2                                                   8                                                      ___        3      3/2        2      5/2        |
             \                                         x         4*x   *(1 + x)   2*x   *(1 + x)                                                                                                         \/ x *(1 + x)    2*x   *(1 + x)    8*x   *(1 + x)/

x^{\operatorname{atan}{\left(\sqrt{x} \right)}} \left(\frac{\left(\frac{2 \operatorname{atan}{\left(\sqrt{x} \right)}}{x} + \frac{\log{\left(x \right)}}{\sqrt{x} \left(x + 1\right)}\right)^{3}}{8} - \frac{3 \left(\frac{2 \operatorname{atan}{\left(\sqrt{x} \right)}}{x} + \frac{\log{\left(x \right)}}{\sqrt{x} \left(x + 1\right)}\right) \left(\frac{4 \operatorname{atan}{\left(\sqrt{x} \right)}}{x^{2}} + \frac{2 \log{\left(x \right)}}{\sqrt{x} \left(x + 1\right)^{2}} + \frac{\log{\left(x \right)}}{x^{\frac{3}{2}} \left(x + 1\right)} - \frac{4}{x^{\frac{3}{2}} \left(x + 1\right)}\right)}{8} + \frac{2 \operatorname{atan}{\left(\sqrt{x} \right)}}{x^{3}} + \frac{\log{\left(x \right)}}{\sqrt{x} \left(x + 1\right)^{3}} + \frac{\log{\left(x \right)}}{2 x^{\frac{3}{2}} \left(x + 1\right)^{2}} - \frac{3}{2 x^{\frac{3}{2}} \left(x + 1\right)^{2}} + \frac{3 \log{\left(x \right)}}{8 x^{\frac{5}{2}} \left(x + 1\right)} - \frac{9}{4 x^{\frac{5}{2}} \left(x + 1\right)}\right)

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Gráfico

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Derivada de y=x^arctg(sqrt(x))

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