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x^sinx+(tanx)^x
Derivada de la función/ x^sin/ x^sinx+(tanx)^x

Derivada de x^sinx+(tanx)^x

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

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Definida a trozos:

Solución

Ha introducido [src] 
 sin(x)      x   
x       + tan (x)
xsin⁡(x)+tan⁡x(x)x^{\sin{\left(x \right)}} + \tan^{x}{\left(x \right)} 
x^sin(x) + tan(x)^x
Solución detallada

  1. diferenciamos xsin⁡(x)+tan⁡x(x)x^{\sin{\left(x \right)}} + \tan^{x}{\left(x \right)} miembro por miembro:

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

      Perola derivada

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

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

      Perola derivada

      xx(log⁡(x)+1)x^{x} \left(\log{\left(x \right)} + 1\right)

    Como resultado de: xx(log⁡(x)+1)+(log⁡(sin⁡(x))+1)sin⁡sin⁡(x)(x)x^{x} \left(\log{\left(x \right)} + 1\right) + \left(\log{\left(\sin{\left(x \right)} \right)} + 1\right) \sin^{\sin{\left(x \right)}}{\left(x \right)}

Respuesta:

xx(log⁡(x)+1)+(log⁡(sin⁡(x))+1)sin⁡sin⁡(x)(x)x^{x} \left(\log{\left(x \right)} + 1\right) + \left(\log{\left(\sin{\left(x \right)} \right)} + 1\right) \sin^{\sin{\left(x \right)}}{\left(x \right)}

Gráfica
02468-8-6-4-2-1010-5000000000000000050000000000000000
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Primera derivada [src] 
                                           /  /       2   \              \
 sin(x) /sin(x)                \      x    |x*\1 + tan (x)/              |
x      *|------ + cos(x)*log(x)| + tan (x)*|--------------- + log(tan(x))|
        \  x                   /           \     tan(x)                  /
xsin⁡(x)(log⁡(x)cos⁡(x)+sin⁡(x)x)+(x(tan⁡2(x)+1)tan⁡(x)+log⁡(tan⁡(x)))tan⁡x(x)x^{\sin{\left(x \right)}} \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) + \left(\frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} + \log{\left(\tan{\left(x \right)} \right)}\right) \tan^{x}{\left(x \right)}
Simplificar
Segunda derivada [src] 
                                                                   2                                                                                                               
                                2   /  /       2   \              \                                                                                /                 /       2   \\
 sin(x) /sin(x)                \    |x*\1 + tan (x)/              |     x       sin(x) /sin(x)                   2*cos(x)\      x    /       2   \ |        2      x*\1 + tan (x)/|
x      *|------ + cos(x)*log(x)|  + |--------------- + log(tan(x))| *tan (x) - x      *|------ + log(x)*sin(x) - --------| + tan (x)*\1 + tan (x)/*|2*x + ------ - ---------------|
        \  x                   /    \     tan(x)                  /                    |   2                        x    |                         |      tan(x)          2       |
                                                                                       \  x                              /                         \                   tan (x)    /
xsin⁡(x)(log⁡(x)cos⁡(x)+sin⁡(x)x)2−xsin⁡(x)(log⁡(x)sin⁡(x)−2cos⁡(x)x+sin⁡(x)x2)+(x(tan⁡2(x)+1)tan⁡(x)+log⁡(tan⁡(x)))2tan⁡x(x)+(tan⁡2(x)+1)(−x(tan⁡2(x)+1)tan⁡2(x)+2x+2tan⁡(x))tan⁡x(x)x^{\sin{\left(x \right)}} \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)^{2} - x^{\sin{\left(x \right)}} \left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{x} + \frac{\sin{\left(x \right)}}{x^{2}}\right) + \left(\frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} + \log{\left(\tan{\left(x \right)} \right)}\right)^{2} \tan^{x}{\left(x \right)} + \left(\tan^{2}{\left(x \right)} + 1\right) \left(- \frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan^{2}{\left(x \right)}} + 2 x + \frac{2}{\tan{\left(x \right)}}\right) \tan^{x}{\left(x \right)}
Simplificar
Tercera derivada [src] 
                                                                   3                   /                               2                    2                    3                           \                                                                                                                                                                                                                               
                                3   /  /       2   \              \                    |                  /       2   \        /       2   \        /       2   \                            |                                                                                                                                                               /  /       2   \              \ /                 /       2   \\
 sin(x) /sin(x)                \    |x*\1 + tan (x)/              |     x         x    |         2      3*\1 + tan (x)/    4*x*\1 + tan (x)/    2*x*\1 + tan (x)/        /       2   \       |    sin(x) /                2*sin(x)   3*sin(x)   3*cos(x)\      sin(x) /sin(x)                \ /sin(x)                   2*cos(x)\        x    /       2   \ |x*\1 + tan (x)/              | |        2      x*\1 + tan (x)/|
x      *|------ + cos(x)*log(x)|  + |--------------- + log(tan(x))| *tan (x) + tan (x)*|6 + 6*tan (x) - ---------------- - ------------------ + ------------------ + 4*x*\1 + tan (x)/*tan(x)| - x      *|cos(x)*log(x) - -------- + -------- + --------| - 3*x      *|------ + cos(x)*log(x)|*|------ + log(x)*sin(x) - --------| + 3*tan (x)*\1 + tan (x)/*|--------------- + log(tan(x))|*|2*x + ------ - ---------------|
        \  x                   /    \     tan(x)                  /                    |                       2                 tan(x)                 3                                    |           |                    3         x           2   |             \  x                   / |   2                        x    |                           \     tan(x)                  / |      tan(x)          2       |
                                                                                       \                    tan (x)                                  tan (x)                                 /           \                   x                     x    /                                      \  x                              /                                                           \                   tan (x)    /
xsin⁡(x)(log⁡(x)cos⁡(x)+sin⁡(x)x)3−3xsin⁡(x)(log⁡(x)cos⁡(x)+sin⁡(x)x)(log⁡(x)sin⁡(x)−2cos⁡(x)x+sin⁡(x)x2)−xsin⁡(x)(log⁡(x)cos⁡(x)+3sin⁡(x)x+3cos⁡(x)x2−2sin⁡(x)x3)+(x(tan⁡2(x)+1)tan⁡(x)+log⁡(tan⁡(x)))3tan⁡x(x)+3(x(tan⁡2(x)+1)tan⁡(x)+log⁡(tan⁡(x)))(tan⁡2(x)+1)(−x(tan⁡2(x)+1)tan⁡2(x)+2x+2tan⁡(x))tan⁡x(x)+(2x(tan⁡2(x)+1)3tan⁡3(x)−4x(tan⁡2(x)+1)2tan⁡(x)+4x(tan⁡2(x)+1)tan⁡(x)−3(tan⁡2(x)+1)2tan⁡2(x)+6tan⁡2(x)+6)tan⁡x(x)x^{\sin{\left(x \right)}} \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)^{3} - 3 x^{\sin{\left(x \right)}} \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{x} + \frac{\sin{\left(x \right)}}{x^{2}}\right) - x^{\sin{\left(x \right)}} \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{3 \sin{\left(x \right)}}{x} + \frac{3 \cos{\left(x \right)}}{x^{2}} - \frac{2 \sin{\left(x \right)}}{x^{3}}\right) + \left(\frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} + \log{\left(\tan{\left(x \right)} \right)}\right)^{3} \tan^{x}{\left(x \right)} + 3 \left(\frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} + \log{\left(\tan{\left(x \right)} \right)}\right) \left(\tan^{2}{\left(x \right)} + 1\right) \left(- \frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan^{2}{\left(x \right)}} + 2 x + \frac{2}{\tan{\left(x \right)}}\right) \tan^{x}{\left(x \right)} + \left(\frac{2 x \left(\tan^{2}{\left(x \right)} + 1\right)^{3}}{\tan^{3}{\left(x \right)}} - \frac{4 x \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\tan{\left(x \right)}} + 4 x \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} - \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\tan^{2}{\left(x \right)}} + 6 \tan^{2}{\left(x \right)} + 6\right) \tan^{x}{\left(x \right)}
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Gráfico
Derivada de x^sinx+(tanx)^x
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