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Expresiones idénticas
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y=x^(2·x-sin(3·x))^(1/2)
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Derivada de la función/ x+sin/ (1/2)/ y=x^(2·x+sin(3·x))^(1/2)

Derivada de y=x^(2·x+sin(3·x))^(1/2)

Solución

Ha introducido [src]

   ________________
 \/ 2*x + sin(3*x) 
x

x^{\sqrt{2 x + \sin{\left(3 x \right)}}}

x^(sqrt(2*x + sin(3*x)))

Solución detallada

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

Perola derivada

$\left(2 x + \sin{\left(3 x \right)}\right)^{\frac{\sqrt{2 x + \sin{\left(3 x \right)}}}{2}} \left(\log{\left(\sqrt{2 x + \sin{\left(3 x \right)}} \right)} + 1\right)$
Simplificamos:

$\frac{\left(2 x + \sin{\left(3 x \right)}\right)^{\frac{\sqrt{2 x + \sin{\left(3 x \right)}}}{2}} \left(\log{\left(2 x + \sin{\left(3 x \right)} \right)} + 2\right)}{2}$

Respuesta:

$\frac{\left(2 x + \sin{\left(3 x \right)}\right)^{\frac{\sqrt{2 x + \sin{\left(3 x \right)}}}{2}} \left(\log{\left(2 x + \sin{\left(3 x \right)} \right)} + 2\right)}{2}$

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

                    /                     /    3*cos(3*x)\       \
   ________________ |  ________________   |1 + ----------|*log(x)|
 \/ 2*x + sin(3*x)  |\/ 2*x + sin(3*x)    \        2     /       |
x                  *|------------------ + -----------------------|
                    |        x                 ________________  |
                    \                        \/ 2*x + sin(3*x)   /

x^{\sqrt{2 x + \sin{\left(3 x \right)}}} \left(\frac{\left(\frac{3 \cos{\left(3 x \right)}}{2} + 1\right) \log{\left(x \right)}}{\sqrt{2 x + \sin{\left(3 x \right)}}} + \frac{\sqrt{2 x + \sin{\left(3 x \right)}}}{x}\right)

Simplificar

Segunda derivada [src]

                    /                                                2                                                                                              \
                    |/    ________________                          \                                                                                               |
                    ||2*\/ 2*x + sin(3*x)    (2 + 3*cos(3*x))*log(x)|                                                                                               |
                    ||-------------------- + -----------------------|                                                                                               |
   ________________ ||         x                  ________________  |      ________________                                                                 2       |
 \/ 2*x + sin(3*x)  |\                          \/ 2*x + sin(3*x)   /    \/ 2*x + sin(3*x)       2 + 3*cos(3*x)       9*log(x)*sin(3*x)     (2 + 3*cos(3*x)) *log(x)|
x                  *|------------------------------------------------- - ------------------ + -------------------- - -------------------- - ------------------------|
                    |                        4                                    2               ________________       ________________                      3/2  |
                    \                                                            x            x*\/ 2*x + sin(3*x)    2*\/ 2*x + sin(3*x)     4*(2*x + sin(3*x))     /

x^{\sqrt{2 x + \sin{\left(3 x \right)}}} \left(\frac{\left(\frac{\left(3 \cos{\left(3 x \right)} + 2\right) \log{\left(x \right)}}{\sqrt{2 x + \sin{\left(3 x \right)}}} + \frac{2 \sqrt{2 x + \sin{\left(3 x \right)}}}{x}\right)^{2}}{4} - \frac{9 \log{\left(x \right)} \sin{\left(3 x \right)}}{2 \sqrt{2 x + \sin{\left(3 x \right)}}} - \frac{\left(3 \cos{\left(3 x \right)} + 2\right)^{2} \log{\left(x \right)}}{4 \left(2 x + \sin{\left(3 x \right)}\right)^{\frac{3}{2}}} + \frac{3 \cos{\left(3 x \right)} + 2}{x \sqrt{2 x + \sin{\left(3 x \right)}}} - \frac{\sqrt{2 x + \sin{\left(3 x \right)}}}{x^{2}}\right)

Simplificar

Tercera derivada [src]

                    /                                                3                                                                                                                                                                                                                                                                                                                                                 \
                    |/    ________________                          \                             /    ________________                          \ /    ________________                   2                                                   \                                                                                                                                                                       |
                    ||2*\/ 2*x + sin(3*x)    (2 + 3*cos(3*x))*log(x)|                             |2*\/ 2*x + sin(3*x)    (2 + 3*cos(3*x))*log(x)| |4*\/ 2*x + sin(3*x)    (2 + 3*cos(3*x)) *log(x)    4*(2 + 3*cos(3*x))    18*log(x)*sin(3*x)|                                                                                                                                                                       |
                    ||-------------------- + -----------------------|                           3*|-------------------- + -----------------------|*|-------------------- + ------------------------ - -------------------- + ------------------|                                                                                                                                                                       |
   ________________ ||         x                  ________________  |        ________________     |         x                  ________________  | |          2                              3/2          ________________     ________________|                                                                                                 2                       3                                             |
 \/ 2*x + sin(3*x)  |\                          \/ 2*x + sin(3*x)   /    2*\/ 2*x + sin(3*x)      \                          \/ 2*x + sin(3*x)   / \         x               (2*x + sin(3*x))         x*\/ 2*x + sin(3*x)    \/ 2*x + sin(3*x) /        27*sin(3*x)          27*cos(3*x)*log(x)       3*(2 + 3*cos(3*x))       3*(2 + 3*cos(3*x))      3*(2 + 3*cos(3*x)) *log(x)   27*(2 + 3*cos(3*x))*log(x)*sin(3*x)|
x                  *|------------------------------------------------- + -------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------ - ---------------------- - -------------------- - ----------------------- - ----------------------- + -------------------------- + -----------------------------------|
                    |                        8                                     3                                                                                   8                                                                                 ________________       ________________      2   ________________                       3/2                       5/2                               3/2       |
                    \                                                             x                                                                                                                                                                2*x*\/ 2*x + sin(3*x)    2*\/ 2*x + sin(3*x)    2*x *\/ 2*x + sin(3*x)    4*x*(2*x + sin(3*x))        8*(2*x + sin(3*x))                4*(2*x + sin(3*x))          /

x^{\sqrt{2 x + \sin{\left(3 x \right)}}} \left(\frac{\left(\frac{\left(3 \cos{\left(3 x \right)} + 2\right) \log{\left(x \right)}}{\sqrt{2 x + \sin{\left(3 x \right)}}} + \frac{2 \sqrt{2 x + \sin{\left(3 x \right)}}}{x}\right)^{3}}{8} - \frac{3 \left(\frac{\left(3 \cos{\left(3 x \right)} + 2\right) \log{\left(x \right)}}{\sqrt{2 x + \sin{\left(3 x \right)}}} + \frac{2 \sqrt{2 x + \sin{\left(3 x \right)}}}{x}\right) \left(\frac{18 \log{\left(x \right)} \sin{\left(3 x \right)}}{\sqrt{2 x + \sin{\left(3 x \right)}}} + \frac{\left(3 \cos{\left(3 x \right)} + 2\right)^{2} \log{\left(x \right)}}{\left(2 x + \sin{\left(3 x \right)}\right)^{\frac{3}{2}}} - \frac{4 \left(3 \cos{\left(3 x \right)} + 2\right)}{x \sqrt{2 x + \sin{\left(3 x \right)}}} + \frac{4 \sqrt{2 x + \sin{\left(3 x \right)}}}{x^{2}}\right)}{8} - \frac{27 \log{\left(x \right)} \cos{\left(3 x \right)}}{2 \sqrt{2 x + \sin{\left(3 x \right)}}} + \frac{27 \left(3 \cos{\left(3 x \right)} + 2\right) \log{\left(x \right)} \sin{\left(3 x \right)}}{4 \left(2 x + \sin{\left(3 x \right)}\right)^{\frac{3}{2}}} + \frac{3 \left(3 \cos{\left(3 x \right)} + 2\right)^{3} \log{\left(x \right)}}{8 \left(2 x + \sin{\left(3 x \right)}\right)^{\frac{5}{2}}} - \frac{27 \sin{\left(3 x \right)}}{2 x \sqrt{2 x + \sin{\left(3 x \right)}}} - \frac{3 \left(3 \cos{\left(3 x \right)} + 2\right)^{2}}{4 x \left(2 x + \sin{\left(3 x \right)}\right)^{\frac{3}{2}}} - \frac{3 \left(3 \cos{\left(3 x \right)} + 2\right)}{2 x^{2} \sqrt{2 x + \sin{\left(3 x \right)}}} + \frac{2 \sqrt{2 x + \sin{\left(3 x \right)}}}{x^{3}}\right)

Simplificar

Gráfico

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Expresiones idénticas

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Expresiones con funciones

Derivada de y=x^(2·x+sin(3·x))^(1/2)

Gráfico:

Definida a trozos:

Solución