Derivada de (x+e)^arctg(sqrtx)

Ha introducido [src]

           /  ___\
       atan\\/ x /
(x + E)

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

(x + E)^atan(sqrt(x))

Solución detallada

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

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

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

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

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

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Segunda derivada [src]

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

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

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Tercera derivada [src]

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

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

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Gráfico

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Derivada de (x+e)^arctg(sqrtx)

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