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x^sin(x+5)
Derivada de la función/ x^sin/ (x+5)/ x^sin(x+5)

Derivada de x^sin(x+5)

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

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Solución

Ha introducido [src] 
 sin(x + 5)
x
xsin⁡(x+5)x^{\sin{\left(x + 5 \right)}} 
x^sin(x + 5)
Solución detallada

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

    Perola derivada

    (log⁡(sin⁡(x+5))+1)sin⁡sin⁡(x+5)(x+5)\left(\log{\left(\sin{\left(x + 5 \right)} \right)} + 1\right) \sin^{\sin{\left(x + 5 \right)}}{\left(x + 5 \right)}

  2. Simplificamos:

    (log⁡(sin⁡(x+5))+1)sin⁡sin⁡(x+5)(x+5)\left(\log{\left(\sin{\left(x + 5 \right)} \right)} + 1\right) \sin^{\sin{\left(x + 5 \right)}}{\left(x + 5 \right)}

Respuesta:

(log⁡(sin⁡(x+5))+1)sin⁡sin⁡(x+5)(x+5)\left(\log{\left(\sin{\left(x + 5 \right)} \right)} + 1\right) \sin^{\sin{\left(x + 5 \right)}}{\left(x + 5 \right)}

Gráfica
02468-8-6-4-2-1010-100100
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Primera derivada [src] 
 sin(x + 5) /sin(x + 5)                    \
x          *|---------- + cos(x + 5)*log(x)|
            \    x                         /
xsin⁡(x+5)(log⁡(x)cos⁡(x+5)+sin⁡(x+5)x)x^{\sin{\left(x + 5 \right)}} \left(\log{\left(x \right)} \cos{\left(x + 5 \right)} + \frac{\sin{\left(x + 5 \right)}}{x}\right)
Simplificar
Segunda derivada [src] 
            /                                2                                                \
 sin(5 + x) |/sin(5 + x)                    \    sin(5 + x)                       2*cos(5 + x)|
x          *||---------- + cos(5 + x)*log(x)|  - ---------- - log(x)*sin(5 + x) + ------------|
            |\    x                         /         2                                x      |
            \                                        x                                        /
xsin⁡(x+5)((log⁡(x)cos⁡(x+5)+sin⁡(x+5)x)2−log⁡(x)sin⁡(x+5)+2cos⁡(x+5)x−sin⁡(x+5)x2)x^{\sin{\left(x + 5 \right)}} \left(\left(\log{\left(x \right)} \cos{\left(x + 5 \right)} + \frac{\sin{\left(x + 5 \right)}}{x}\right)^{2} - \log{\left(x \right)} \sin{\left(x + 5 \right)} + \frac{2 \cos{\left(x + 5 \right)}}{x} - \frac{\sin{\left(x + 5 \right)}}{x^{2}}\right)
Simplificar
Tercera derivada [src] 
            /                                3                                                                                                                                                      \
 sin(5 + x) |/sin(5 + x)                    \                        3*sin(5 + x)   3*cos(5 + x)     /sin(5 + x)                    \ /sin(5 + x)                       2*cos(5 + x)\   2*sin(5 + x)|
x          *||---------- + cos(5 + x)*log(x)|  - cos(5 + x)*log(x) - ------------ - ------------ - 3*|---------- + cos(5 + x)*log(x)|*|---------- + log(x)*sin(5 + x) - ------------| + ------------|
            |\    x                         /                             x               2          \    x                         / |     2                                x      |         3     |
            \                                                                            x                                            \    x                                        /        x      /
xsin⁡(x+5)((log⁡(x)cos⁡(x+5)+sin⁡(x+5)x)3−3(log⁡(x)cos⁡(x+5)+sin⁡(x+5)x)(log⁡(x)sin⁡(x+5)−2cos⁡(x+5)x+sin⁡(x+5)x2)−log⁡(x)cos⁡(x+5)−3sin⁡(x+5)x−3cos⁡(x+5)x2+2sin⁡(x+5)x3)x^{\sin{\left(x + 5 \right)}} \left(\left(\log{\left(x \right)} \cos{\left(x + 5 \right)} + \frac{\sin{\left(x + 5 \right)}}{x}\right)^{3} - 3 \left(\log{\left(x \right)} \cos{\left(x + 5 \right)} + \frac{\sin{\left(x + 5 \right)}}{x}\right) \left(\log{\left(x \right)} \sin{\left(x + 5 \right)} - \frac{2 \cos{\left(x + 5 \right)}}{x} + \frac{\sin{\left(x + 5 \right)}}{x^{2}}\right) - \log{\left(x \right)} \cos{\left(x + 5 \right)} - \frac{3 \sin{\left(x + 5 \right)}}{x} - \frac{3 \cos{\left(x + 5 \right)}}{x^{2}} + \frac{2 \sin{\left(x + 5 \right)}}{x^{3}}\right)
Simplificar
Gráfico
Derivada de x^sin(x+5)
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