Sr Examen

Derivada de y=(sin√x)^e^x

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

interior superior

Definida a trozos:

Solución

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

    Perola derivada

  2. Simplificamos:


Respuesta:

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