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sin(x)^4
sin(x/3+3)+2*x
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sin(x^2+3)
Raíz cuadrada sqrt
sqrt(x*2)
sqrt(log(6*x-1))
sqrt((x-1)/2)
sqrt(4-3*(sin(t^(3)))*(cos(t)^(2))^(2))
sqrt(3*y)

Derivada de la función/ log(sin(sqrt(x)))/ x*(sin(sqrt(x)))^log(sin(sqrt(x)))

Derivada de x*(sin(sqrt(x)))^log(sin(sqrt(x)))

Solución

Ha introducido [src]

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

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

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

Solución detallada

Se aplica la regla de la derivada de una multiplicación:

$\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$

$f{\left(x \right)} = x$ ; calculamos $\frac{d}{d x} f{\left(x \right)}$ :
1. Según el principio, aplicamos: $x$ tenemos $1$
$g{\left(x \right)} = \sin^{\log{\left(\sin{\left(\sqrt{x} \right)} \right)}}{\left(\sqrt{x} \right)}$ ; calculamos $\frac{d}{d x} g{\left(x \right)}$ :
1. No logro encontrar los pasos en la búsqueda de esta derivada.
  
  Perola derivada
  
  $\left(\log{\left(\log{\left(\sin{\left(\sqrt{x} \right)} \right)} \right)} + 1\right) \log{\left(\sin{\left(\sqrt{x} \right)} \right)}^{\log{\left(\sin{\left(\sqrt{x} \right)} \right)}}$
Como resultado de: $x \left(\log{\left(\log{\left(\sin{\left(\sqrt{x} \right)} \right)} \right)} + 1\right) \log{\left(\sin{\left(\sqrt{x} \right)} \right)}^{\log{\left(\sin{\left(\sqrt{x} \right)} \right)}} + \sin^{\log{\left(\sin{\left(\sqrt{x} \right)} \right)}}{\left(\sqrt{x} \right)}$

Respuesta:

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

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

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

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

Simplificar

Segunda derivada [src]

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

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

Simplificar

Tercera derivada [src]

                             /  /       /   /  ___\\        2/  ___\          3/  ___\            /  ___\         3/  ___\    /   /  ___\\        3/  ___\    3/   /  ___\\        2/  ___\    /   /  ___\\        /  ___\    /   /  ___\\        /  ___\    /   /  ___\\        2/  ___\    2/   /  ___\\        3/  ___\    2/   /  ___\\        2/   /  ___\\    /  ___\\                                                                                                                                      \
                             |  |  3*log\sin\\/ x //   3*cos \\/ x /     3*cos \\/ x /       3*cos\\/ x /    8*cos \\/ x /*log\sin\\/ x //   4*cos \\/ x /*log \sin\\/ x //   3*cos \\/ x /*log\sin\\/ x //   3*cos\\/ x /*log\sin\\/ x //   2*cos\\/ x /*log\sin\\/ x //   6*cos \\/ x /*log \sin\\/ x //   6*cos \\/ x /*log \sin\\/ x //   6*log \sin\\/ x //*cos\\/ x /|                                                                                                                                      |
                /   /  ___\\ |x*|- ----------------- + -------------- + ---------------- + --------------- - ----------------------------- - ------------------------------ - ----------------------------- - ---------------------------- - ---------------------------- + ------------------------------ + ------------------------------ + -----------------------------|                                                                                                                                      |
             log\sin\\/ x // |  |           2           2    2/  ___\    3/2    3/  ___\    3/2    /  ___\           3/2    3/  ___\                 3/2    3/  ___\                   2    2/  ___\                 5/2    /  ___\                 3/2    /  ___\                   2    2/  ___\                   3/2    3/  ___\                  3/2    /  ___\       |        /   /  ___\\         2/  ___\         2/  ___\    2/   /  ___\\        2/  ___\    /   /  ___\\        /  ___\    /   /  ___\\|
 /   /  ___\\                |  \          x           x *sin \\/ x /   x   *sin \\/ x /   x   *sin\\/ x /          x   *sin \\/ x /                x   *sin \\/ x /                  x *sin \\/ x /                x   *sin\\/ x /                x   *sin\\/ x /                  x *sin \\/ x /                  x   *sin \\/ x /                 x   *sin\\/ x /       /   3*log\sin\\/ x //    3*cos \\/ x /    3*cos \\/ x /*log \sin\\/ x //   3*cos \\/ x /*log\sin\\/ x //   3*cos\\/ x /*log\sin\\/ x //|
-\sin\\/ x //               *|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------- - --------------- - ------------------------------ + ----------------------------- + ----------------------------|
                             |                                                                                                                                                                      4                                                                                                                                                                                 2*x                 2/  ___\                2/  ___\                          2/  ___\                  3/2    /  ___\      |
                             \                                                                                                                                                                                                                                                                                                                                                                     2*x*sin \\/ x /           x*sin \\/ x /                   2*x*sin \\/ x /               2*x   *sin\\/ x /      /

$$- \left(\frac{x \left(\frac{6 \log{\left(\sin{\left(\sqrt{x} \right)} \right)}^{2} \cos^{2}{\left(\sqrt{x} \right)}}{x^{2} \sin^{2}{\left(\sqrt{x} \right)}} - \frac{3 \log{\left(\sin{\left(\sqrt{x} \right)} \right)}}{x^{2}} - \frac{3 \log{\left(\sin{\left(\sqrt{x} \right)} \right)} \cos^{2}{\left(\sqrt{x} \right)}}{x^{2} \sin^{2}{\left(\sqrt{x} \right)}} + \frac{3 \cos^{2}{\left(\sqrt{x} \right)}}{x^{2} \sin^{2}{\left(\sqrt{x} \right)}} - \frac{4 \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{6 \log{\left(\sin{\left(\sqrt{x} \right)} \right)}^{2} \cos{\left(\sqrt{x} \right)}}{x^{\frac{3}{2}} \sin{\left(\sqrt{x} \right)}} + \frac{6 \log{\left(\sin{\left(\sqrt{x} \right)} \right)}^{2} \cos^{3}{\left(\sqrt{x} \right)}}{x^{\frac{3}{2}} \sin^{3}{\left(\sqrt{x} \right)}} - \frac{2 \log{\left(\sin{\left(\sqrt{x} \right)} \right)} \cos{\left(\sqrt{x} \right)}}{x^{\frac{3}{2}} \sin{\left(\sqrt{x} \right)}} - \frac{8 \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)}}{x^{\frac{3}{2}} \sin{\left(\sqrt{x} \right)}} + \frac{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)} \cos{\left(\sqrt{x} \right)}}{x^{\frac{5}{2}} \sin{\left(\sqrt{x} \right)}}\right)}{4} - \frac{3 \log{\left(\sin{\left(\sqrt{x} \right)} \right)}^{2} \cos^{2}{\left(\sqrt{x} \right)}}{x \sin^{2}{\left(\sqrt{x} \right)}} + \frac{3 \log{\left(\sin{\left(\sqrt{x} \right)} \right)}}{2 x} + \frac{3 \log{\left(\sin{\left(\sqrt{x} \right)} \right)} \cos^{2}{\left(\sqrt{x} \right)}}{2 x \sin^{2}{\left(\sqrt{x} \right)}} - \frac{3 \cos^{2}{\left(\sqrt{x} \right)}}{2 x \sin^{2}{\left(\sqrt{x} \right)}} + \frac{3 \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

Gráfico

Derivada de x*(sin(sqrt(x)))^log(sin(sqrt(x)))

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Expresiones con funciones

Derivada de x*(sin(sqrt(x)))^log(sin(sqrt(x)))

Gráfico:

Definida a trozos:

Solución