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y=(sin(2x)^sqrtx)
Derivada de la función/ sqrtx/ sin(2x)/ y=(sin(2x)^sqrtx)

Derivada de y=(sin(2x)^sqrtx)

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

Ha introducido [src] 
            ___
          \/ x 
(sin(2*x))
sin⁡x(2x)\sin^{\sqrt{x}}{\left(2 x \right)} 
sin(2*x)^(sqrt(x))
Solución detallada

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

    Perola derivada

    xx2(log⁡(x)+1)x^{\frac{\sqrt{x}}{2}} \left(\log{\left(\sqrt{x} \right)} + 1\right)

  2. Simplificamos:

    xx2(log⁡(x)+2)2\frac{x^{\frac{\sqrt{x}}{2}} \left(\log{\left(x \right)} + 2\right)}{2}

Respuesta:

xx2(log⁡(x)+2)2\frac{x^{\frac{\sqrt{x}}{2}} \left(\log{\left(x \right)} + 2\right)}{2}

Gráfica
02468-8-6-4-2-10105-5
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
            ___ /                    ___         \
          \/ x  |log(sin(2*x))   2*\/ x *cos(2*x)|
(sin(2*x))     *|------------- + ----------------|
                |       ___          sin(2*x)    |
                \   2*\/ x                       /
(2xcos⁡(2x)sin⁡(2x)+log⁡(sin⁡(2x))2x)sin⁡x(2x)\left(\frac{2 \sqrt{x} \cos{\left(2 x \right)}}{\sin{\left(2 x \right)}} + \frac{\log{\left(\sin{\left(2 x \right)} \right)}}{2 \sqrt{x}}\right) \sin^{\sqrt{x}}{\left(2 x \right)}
Simplificar
Segunda derivada [src] 
                /                                              2                                                     \
                |            /                    ___         \                                                      |
                |            |log(sin(2*x))   4*\/ x *cos(2*x)|                                                      |
                |            |------------- + ----------------|                                                      |
            ___ |            |      ___           sin(2*x)    |                        ___    2                      |
          \/ x  |      ___   \    \/ x                        /    log(sin(2*x))   4*\/ x *cos (2*x)     2*cos(2*x)  |
(sin(2*x))     *|- 4*\/ x  + ----------------------------------- - ------------- - ----------------- + --------------|
                |                             4                           3/2             2              ___         |
                \                                                      4*x             sin (2*x)       \/ x *sin(2*x)/
(−4x−4xcos⁡2(2x)sin⁡2(2x)+(4xcos⁡(2x)sin⁡(2x)+log⁡(sin⁡(2x))x)24+2cos⁡(2x)xsin⁡(2x)−log⁡(sin⁡(2x))4x32)sin⁡x(2x)\left(- 4 \sqrt{x} - \frac{4 \sqrt{x} \cos^{2}{\left(2 x \right)}}{\sin^{2}{\left(2 x \right)}} + \frac{\left(\frac{4 \sqrt{x} \cos{\left(2 x \right)}}{\sin{\left(2 x \right)}} + \frac{\log{\left(\sin{\left(2 x \right)} \right)}}{\sqrt{x}}\right)^{2}}{4} + \frac{2 \cos{\left(2 x \right)}}{\sqrt{x} \sin{\left(2 x \right)}} - \frac{\log{\left(\sin{\left(2 x \right)} \right)}}{4 x^{\frac{3}{2}}}\right) \sin^{\sqrt{x}}{\left(2 x \right)}
Simplificar
Tercera derivada [src] 
                /                                            3                                                                                                                                                                                                       \
                |          /                    ___         \      /                    ___         \ /                                                 ___    2     \                                                                                               |
                |          |log(sin(2*x))   4*\/ x *cos(2*x)|      |log(sin(2*x))   4*\/ x *cos(2*x)| |     ___   log(sin(2*x))     8*cos(2*x)     16*\/ x *cos (2*x)|                                                                                               |
                |          |------------- + ----------------|    3*|------------- + ----------------|*|16*\/ x  + ------------- - -------------- + ------------------|                                                                                               |
            ___ |          |      ___           sin(2*x)    |      |      ___           sin(2*x)    | |                 3/2         ___                   2          |                            2               ___    3             ___                           |
          \/ x  |    6     \    \/ x                        /      \    \/ x                        / \                x          \/ x *sin(2*x)       sin (2*x)     /   3*log(sin(2*x))     6*cos (2*x)     16*\/ x *cos (2*x)   16*\/ x *cos(2*x)      3*cos(2*x)  |
(sin(2*x))     *|- ----- + ----------------------------------- - ----------------------------------------------------------------------------------------------------- + --------------- - --------------- + ------------------ + ----------------- - ---------------|
                |    ___                    8                                                                      8                                                             5/2         ___    2               3                  sin(2*x)          3/2         |
                \  \/ x                                                                                                                                                       8*x          \/ x *sin (2*x)       sin (2*x)                            2*x   *sin(2*x)/
(16xcos⁡(2x)sin⁡(2x)+16xcos⁡3(2x)sin⁡3(2x)+(4xcos⁡(2x)sin⁡(2x)+log⁡(sin⁡(2x))x)38−3(4xcos⁡(2x)sin⁡(2x)+log⁡(sin⁡(2x))x)(16x+16xcos⁡2(2x)sin⁡2(2x)−8cos⁡(2x)xsin⁡(2x)+log⁡(sin⁡(2x))x32)8−6x−6cos⁡2(2x)xsin⁡2(2x)−3cos⁡(2x)2x32sin⁡(2x)+3log⁡(sin⁡(2x))8x52)sin⁡x(2x)\left(\frac{16 \sqrt{x} \cos{\left(2 x \right)}}{\sin{\left(2 x \right)}} + \frac{16 \sqrt{x} \cos^{3}{\left(2 x \right)}}{\sin^{3}{\left(2 x \right)}} + \frac{\left(\frac{4 \sqrt{x} \cos{\left(2 x \right)}}{\sin{\left(2 x \right)}} + \frac{\log{\left(\sin{\left(2 x \right)} \right)}}{\sqrt{x}}\right)^{3}}{8} - \frac{3 \left(\frac{4 \sqrt{x} \cos{\left(2 x \right)}}{\sin{\left(2 x \right)}} + \frac{\log{\left(\sin{\left(2 x \right)} \right)}}{\sqrt{x}}\right) \left(16 \sqrt{x} + \frac{16 \sqrt{x} \cos^{2}{\left(2 x \right)}}{\sin^{2}{\left(2 x \right)}} - \frac{8 \cos{\left(2 x \right)}}{\sqrt{x} \sin{\left(2 x \right)}} + \frac{\log{\left(\sin{\left(2 x \right)} \right)}}{x^{\frac{3}{2}}}\right)}{8} - \frac{6}{\sqrt{x}} - \frac{6 \cos^{2}{\left(2 x \right)}}{\sqrt{x} \sin^{2}{\left(2 x \right)}} - \frac{3 \cos{\left(2 x \right)}}{2 x^{\frac{3}{2}} \sin{\left(2 x \right)}} + \frac{3 \log{\left(\sin{\left(2 x \right)} \right)}}{8 x^{\frac{5}{2}}}\right) \sin^{\sqrt{x}}{\left(2 x \right)}
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Gráfico
Derivada de y=(sin(2x)^sqrtx)
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