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y=(sin(sqrt(x)))^(e^(2x))

Derivada de y=(sin(sqrt(x)))^(e^(2x))

Función f() - derivada -er orden en el punto
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Gráfico:

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Solución

Ha introducido [src]
            / 2*x\
            \E   /
/   /  ___\\      
\sin\\/ x //      
$$\sin^{e^{2 x}}{\left(\sqrt{x} \right)}$$
sin(sqrt(x))^(E^(2*x))
Solución detallada
  1. No logro encontrar los pasos en la búsqueda de esta derivada.

    Perola derivada

  2. Simplificamos:


Respuesta:

Gráfica
Primera derivada [src]
            / 2*x\                                              
            \E   / /                             /  ___\  2*x  \
/   /  ___\\       |   2*x    /   /  ___\\    cos\\/ x /*e     |
\sin\\/ x //      *|2*e   *log\sin\\/ x // + ------------------|
                   |                             ___    /  ___\|
                   \                         2*\/ x *sin\\/ x //
$$\left(2 e^{2 x} \log{\left(\sin{\left(\sqrt{x} \right)} \right)} + \frac{e^{2 x} \cos{\left(\sqrt{x} \right)}}{2 \sqrt{x} \sin{\left(\sqrt{x} \right)}}\right) \sin^{e^{2 x}}{\left(\sqrt{x} \right)}$$
Segunda derivada [src]
                   /                                                                2                                                              \     
                   |                          /                          /  ___\   \                                                               |     
                   |                          |     /   /  ___\\      cos\\/ x /   |   2*x                                                         |     
            / 2*x\ |                          |4*log\sin\\/ x // + ----------------| *e                                                            |     
            \e   / |                          |                      ___    /  ___\|                /  ___\          2/  ___\            /  ___\   |     
/   /  ___\\       |     /   /  ___\\    1    \                    \/ x *sin\\/ x //           2*cos\\/ x /       cos \\/ x /         cos\\/ x /   |  2*x
\sin\\/ x //      *|4*log\sin\\/ x // - --- + -------------------------------------------- + ---------------- - --------------- - -----------------|*e   
                   |                    4*x                        4                           ___    /  ___\          2/  ___\      3/2    /  ___\|     
                   \                                                                         \/ x *sin\\/ x /   4*x*sin \\/ x /   4*x   *sin\\/ x //     
$$\left(\frac{\left(4 \log{\left(\sin{\left(\sqrt{x} \right)} \right)} + \frac{\cos{\left(\sqrt{x} \right)}}{\sqrt{x} \sin{\left(\sqrt{x} \right)}}\right)^{2} e^{2 x}}{4} + 4 \log{\left(\sin{\left(\sqrt{x} \right)} \right)} - \frac{1}{4 x} - \frac{\cos^{2}{\left(\sqrt{x} \right)}}{4 x \sin^{2}{\left(\sqrt{x} \right)}} + \frac{2 \cos{\left(\sqrt{x} \right)}}{\sqrt{x} \sin{\left(\sqrt{x} \right)}} - \frac{\cos{\left(\sqrt{x} \right)}}{4 x^{\frac{3}{2}} \sin{\left(\sqrt{x} \right)}}\right) e^{2 x} \sin^{e^{2 x}}{\left(\sqrt{x} \right)}$$
Tercera derivada [src]
                   /                                                                       3                                                                                                                                                                                                                                                        \     
                   |                                 /                          /  ___\   \                                                                    /                          /  ___\   \ /                             2/  ___\          /  ___\            /  ___\  \                                                                 |     
                   |                                 |     /   /  ___\\      cos\\/ x /   |   4*x                                                              |     /   /  ___\\      cos\\/ x /   | |1         /   /  ___\\    cos \\/ x /       cos\\/ x /       8*cos\\/ x /  |  2*x                                                            |     
            / 2*x\ |                                 |4*log\sin\\/ x // + ----------------| *e                                                               3*|4*log\sin\\/ x // + ----------------|*|- - 16*log\sin\\/ x // + ------------- + --------------- - ----------------|*e                                                               |     
            \e   / |                                 |                      ___    /  ___\|                /  ___\             /  ___\           2/  ___\      |                      ___    /  ___\| |x                             2/  ___\    3/2    /  ___\     ___    /  ___\|              3/  ___\             2/  ___\             /  ___\  |     
/   /  ___\\       |     /   /  ___\\    3     3     \                    \/ x *sin\\/ x //           6*cos\\/ x /        5*cos\\/ x /      3*cos \\/ x /      \                    \/ x *sin\\/ x // \                         x*sin \\/ x /   x   *sin\\/ x /   \/ x *sin\\/ x //           cos \\/ x /        3*cos \\/ x /        3*cos\\/ x /  |  2*x
\sin\\/ x //      *|8*log\sin\\/ x // - --- + ---- + -------------------------------------------- + ---------------- - ----------------- - --------------- - --------------------------------------------------------------------------------------------------------------------------- + ------------------ + ---------------- + -----------------|*e   
                   |                    2*x      2                        8                           ___    /  ___\      3/2    /  ___\          2/  ___\                                                                8                                                                   3/2    3/  ___\      2    2/  ___\      5/2    /  ___\|     
                   \                          8*x                                                   \/ x *sin\\/ x /   4*x   *sin\\/ x /   2*x*sin \\/ x /                                                                                                                                 4*x   *sin \\/ x /   8*x *sin \\/ x /   8*x   *sin\\/ x //     
$$\left(\frac{\left(4 \log{\left(\sin{\left(\sqrt{x} \right)} \right)} + \frac{\cos{\left(\sqrt{x} \right)}}{\sqrt{x} \sin{\left(\sqrt{x} \right)}}\right)^{3} e^{4 x}}{8} - \frac{3 \left(4 \log{\left(\sin{\left(\sqrt{x} \right)} \right)} + \frac{\cos{\left(\sqrt{x} \right)}}{\sqrt{x} \sin{\left(\sqrt{x} \right)}}\right) \left(- 16 \log{\left(\sin{\left(\sqrt{x} \right)} \right)} + \frac{1}{x} + \frac{\cos^{2}{\left(\sqrt{x} \right)}}{x \sin^{2}{\left(\sqrt{x} \right)}} - \frac{8 \cos{\left(\sqrt{x} \right)}}{\sqrt{x} \sin{\left(\sqrt{x} \right)}} + \frac{\cos{\left(\sqrt{x} \right)}}{x^{\frac{3}{2}} \sin{\left(\sqrt{x} \right)}}\right) e^{2 x}}{8} + 8 \log{\left(\sin{\left(\sqrt{x} \right)} \right)} - \frac{3}{2 x} - \frac{3 \cos^{2}{\left(\sqrt{x} \right)}}{2 x \sin^{2}{\left(\sqrt{x} \right)}} + \frac{3}{8 x^{2}} + \frac{3 \cos^{2}{\left(\sqrt{x} \right)}}{8 x^{2} \sin^{2}{\left(\sqrt{x} \right)}} + \frac{6 \cos{\left(\sqrt{x} \right)}}{\sqrt{x} \sin{\left(\sqrt{x} \right)}} - \frac{5 \cos{\left(\sqrt{x} \right)}}{4 x^{\frac{3}{2}} \sin{\left(\sqrt{x} \right)}} + \frac{\cos^{3}{\left(\sqrt{x} \right)}}{4 x^{\frac{3}{2}} \sin^{3}{\left(\sqrt{x} \right)}} + \frac{3 \cos{\left(\sqrt{x} \right)}}{8 x^{\frac{5}{2}} \sin{\left(\sqrt{x} \right)}}\right) e^{2 x} \sin^{e^{2 x}}{\left(\sqrt{x} \right)}$$
Gráfico
Derivada de y=(sin(sqrt(x)))^(e^(2x))