Derivada de y=(sin√x)^(ln(sin√x))

Ha introducido [src]

               /   /  ___\\
            log\sin\\/ x //
/   /  ___\\               
\sin\\/ x //

$$\sin^{\log{\left(\sin{\left(\sqrt{x} \right)} \right)}}{\left(\sqrt{x} \right)}$$

sin(sqrt(x))^log(sin(sqrt(x)))

Solución detallada

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

Perola derivada

$\left(\log{\left(\log{\left(\sin{\left(\sqrt{x} \right)} \right)} \right)} + 1\right) \log{\left(\sin{\left(\sqrt{x} \right)} \right)}^{\log{\left(\sin{\left(\sqrt{x} \right)} \right)}}$

Respuesta:

$\left(\log{\left(\log{\left(\sin{\left(\sqrt{x} \right)} \right)} \right)} + 1\right) \log{\left(\sin{\left(\sqrt{x} \right)} \right)}^{\log{\left(\sin{\left(\sqrt{x} \right)} \right)}}$

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

               /   /  ___\\                           
            log\sin\\/ x //                           
/   /  ___\\                   /  ___\    /   /  ___\\
\sin\\/ x //               *cos\\/ x /*log\sin\\/ x //
------------------------------------------------------
                     ___    /  ___\                   
                   \/ x *sin\\/ x /

$$\frac{\log{\left(\sin{\left(\sqrt{x} \right)} \right)} \sin^{\log{\left(\sin{\left(\sqrt{x} \right)} \right)}}{\left(\sqrt{x} \right)} \cos{\left(\sqrt{x} \right)}}{\sqrt{x} \sin{\left(\sqrt{x} \right)}}$$

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Segunda derivada [src]

               /   /  ___\\                                                                                                                                
            log\sin\\/ x // /     /   /  ___\\        2/  ___\        2/  ___\    2/   /  ___\\      2/  ___\    /   /  ___\\      /  ___\    /   /  ___\\\
/   /  ___\\                |  log\sin\\/ x //     cos \\/ x /     cos \\/ x /*log \sin\\/ x //   cos \\/ x /*log\sin\\/ x //   cos\\/ x /*log\sin\\/ x //|
\sin\\/ x //               *|- --------------- + --------------- + ---------------------------- - --------------------------- - --------------------------|
                            |        2*x                2/  ___\               2/  ___\                        2/  ___\                3/2    /  ___\     |
                            \                    2*x*sin \\/ x /          x*sin \\/ x /                 2*x*sin \\/ x /             2*x   *sin\\/ x /     /

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

Simplificar

Tercera derivada [src]

               /   /  ___\\                                                                                                                                                                                                                                                                                                                                             
            log\sin\\/ x // /     /   /  ___\\         2/  ___\            3/  ___\              /  ___\        3/  ___\    3/   /  ___\\      /  ___\    /   /  ___\\        3/  ___\    /   /  ___\\        2/  ___\    2/   /  ___\\        3/  ___\    2/   /  ___\\        2/   /  ___\\    /  ___\        2/  ___\    /   /  ___\\        /  ___\    /   /  ___\\\
/   /  ___\\                |3*log\sin\\/ x //    3*cos \\/ x /       3*cos \\/ x /         3*cos\\/ x /     cos \\/ x /*log \sin\\/ x //   cos\\/ x /*log\sin\\/ x //   2*cos \\/ x /*log\sin\\/ x //   3*cos \\/ x /*log \sin\\/ x //   3*cos \\/ x /*log \sin\\/ x //   3*log \sin\\/ x //*cos\\/ x /   3*cos \\/ x /*log\sin\\/ x //   3*cos\\/ x /*log\sin\\/ x //|
\sin\\/ x //               *|----------------- - ---------------- - ------------------ - ----------------- + ---------------------------- + -------------------------- + ----------------------------- - ------------------------------ - ------------------------------ - ----------------------------- + ----------------------------- + ----------------------------|
                            |          2            2    2/  ___\      3/2    3/  ___\      3/2    /  ___\          3/2    3/  ___\                3/2    /  ___\                3/2    3/  ___\                   2    2/  ___\                   3/2    3/  ___\                  3/2    /  ___\                   2    2/  ___\                 5/2    /  ___\      |
                            \       4*x          4*x *sin \\/ x /   4*x   *sin \\/ x /   4*x   *sin\\/ x /         x   *sin \\/ x /             2*x   *sin\\/ x /               x   *sin \\/ x /                2*x *sin \\/ x /                2*x   *sin \\/ x /               2*x   *sin\\/ x /                4*x *sin \\/ x /              4*x   *sin\\/ x /      /

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

Simplificar

3-я производная [src]

               /   /  ___\\                                                                                                                                                                                                                                                                                                                                             
            log\sin\\/ x // /     /   /  ___\\         2/  ___\            3/  ___\              /  ___\        3/  ___\    3/   /  ___\\      /  ___\    /   /  ___\\        3/  ___\    /   /  ___\\        2/  ___\    2/   /  ___\\        3/  ___\    2/   /  ___\\        2/   /  ___\\    /  ___\        2/  ___\    /   /  ___\\        /  ___\    /   /  ___\\\
/   /  ___\\                |3*log\sin\\/ x //    3*cos \\/ x /       3*cos \\/ x /         3*cos\\/ x /     cos \\/ x /*log \sin\\/ x //   cos\\/ x /*log\sin\\/ x //   2*cos \\/ x /*log\sin\\/ x //   3*cos \\/ x /*log \sin\\/ x //   3*cos \\/ x /*log \sin\\/ x //   3*log \sin\\/ x //*cos\\/ x /   3*cos \\/ x /*log\sin\\/ x //   3*cos\\/ x /*log\sin\\/ x //|
\sin\\/ x //               *|----------------- - ---------------- - ------------------ - ----------------- + ---------------------------- + -------------------------- + ----------------------------- - ------------------------------ - ------------------------------ - ----------------------------- + ----------------------------- + ----------------------------|
                            |          2            2    2/  ___\      3/2    3/  ___\      3/2    /  ___\          3/2    3/  ___\                3/2    /  ___\                3/2    3/  ___\                   2    2/  ___\                   3/2    3/  ___\                  3/2    /  ___\                   2    2/  ___\                 5/2    /  ___\      |
                            \       4*x          4*x *sin \\/ x /   4*x   *sin \\/ x /   4*x   *sin\\/ x /         x   *sin \\/ x /             2*x   *sin\\/ x /               x   *sin \\/ x /                2*x *sin \\/ x /                2*x   *sin \\/ x /               2*x   *sin\\/ x /                4*x *sin \\/ x /              4*x   *sin\\/ x /      /

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

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Gráfico

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Derivada de y=(sin√x)^(ln(sin√x))

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