Derivada de ✓(x^tanx)

Solución

Ha introducido [src]

   _________
  /  tan(x) 
\/  x

$$\sqrt{x^{\tan{\left(x \right)}}}$$

sqrt(x^tan(x))

Solución detallada

Sustituimos $u = x^{\tan{\left(x \right)}}$ .
Según el principio, aplicamos: $\sqrt{u}$ tenemos $\frac{1}{2 \sqrt{u}}$
Luego se aplica una cadena de reglas. Multiplicamos por $\frac{d}{d x} x^{\tan{\left(x \right)}}$ :
1. No logro encontrar los pasos en la búsqueda de esta derivada.
  
  Perola derivada
  
  $\left(\log{\left(\tan{\left(x \right)} \right)} + 1\right) \tan^{\tan{\left(x \right)}}{\left(x \right)}$
Como resultado de la secuencia de reglas:

$\frac{\left(\log{\left(\tan{\left(x \right)} \right)} + 1\right) \tan^{\tan{\left(x \right)}}{\left(x \right)}}{2 \sqrt{x^{\tan{\left(x \right)}}}}$

Respuesta:

$\frac{\left(\log{\left(\tan{\left(x \right)} \right)} + 1\right) \tan^{\tan{\left(x \right)}}{\left(x \right)}}{2 \sqrt{x^{\tan{\left(x \right)}}}}$

Gráfica

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Trazar el gráfico f'(x)

Primera derivada [src]

   _________ /         /       2   \       \
  /  tan(x)  |tan(x)   \1 + tan (x)/*log(x)|
\/  x       *|------ + --------------------|
             \ 2*x              2          /

$$\left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)}}{2} + \frac{\tan{\left(x \right)}}{2 x}\right) \sqrt{x^{\tan{\left(x \right)}}}$$

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Segunda derivada [src]

             /                               2                                                     \
             |/tan(x)   /       2   \       \                                                      |
   _________ ||------ + \1 + tan (x)/*log(x)|           2                                          |
  /  tan(x)  |\  x                          /    1 + tan (x)   tan(x)   /       2   \              |
\/  x       *|-------------------------------- + ----------- - ------ + \1 + tan (x)/*log(x)*tan(x)|
             |               4                        x            2                               |
             \                                                  2*x                                /

$$\left(\frac{\left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right)^{2}}{4} + \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \tan{\left(x \right)} + \frac{\tan^{2}{\left(x \right)} + 1}{x} - \frac{\tan{\left(x \right)}}{2 x^{2}}\right) \sqrt{x^{\tan{\left(x \right)}}}$$

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Tercera derivada [src]

             /                                                                                                                        /             /       2   \                                \                                                          \
             |                               3                                                        /tan(x)   /       2   \       \ |  tan(x)   2*\1 + tan (x)/     /       2   \              |                                                          |
             |/tan(x)   /       2   \       \                                                       3*|------ + \1 + tan (x)/*log(x)|*|- ------ + --------------- + 2*\1 + tan (x)/*log(x)*tan(x)|                                                          |
   _________ ||------ + \1 + tan (x)/*log(x)|                          2            /       2   \     \  x                          / |     2            x                                       |                                      /       2   \       |
  /  tan(x)  |\  x                          /    tan(x)   /       2   \           3*\1 + tan (x)/                                     \    x                                                     /        2    /       2   \          3*\1 + tan (x)/*tan(x)|
\/  x       *|-------------------------------- + ------ + \1 + tan (x)/ *log(x) - --------------- + ---------------------------------------------------------------------------------------------- + 2*tan (x)*\1 + tan (x)/*log(x) + ----------------------|
             |               8                      3                                      2                                                      4                                                                                             x           |
             \                                     x                                    2*x                                                                                                                                                                 /

$$\left(\frac{\left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right)^{3}}{8} + \frac{3 \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right) \left(2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \tan{\left(x \right)} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)}{x} - \frac{\tan{\left(x \right)}}{x^{2}}\right)}{4} + \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(x \right)} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \tan^{2}{\left(x \right)} + \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{x} - \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right)}{2 x^{2}} + \frac{\tan{\left(x \right)}}{x^{3}}\right) \sqrt{x^{\tan{\left(x \right)}}}$$

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Gráfico

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Derivada de ✓(x^tanx)

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Solución