Sr Examen

Derivada de x^sin(x+3)

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

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Solución

Ha introducido [src]
 sin(x + 3)
x          
xsin(x+3)x^{\sin{\left(x + 3 \right)}}
x^sin(x + 3)
Solución detallada
  1. No logro encontrar los pasos en la búsqueda de esta derivada.

    Perola derivada

    (log(sin(x+3))+1)sinsin(x+3)(x+3)\left(\log{\left(\sin{\left(x + 3 \right)} \right)} + 1\right) \sin^{\sin{\left(x + 3 \right)}}{\left(x + 3 \right)}

  2. Simplificamos:

    (log(sin(x+3))+1)sinsin(x+3)(x+3)\left(\log{\left(\sin{\left(x + 3 \right)} \right)} + 1\right) \sin^{\sin{\left(x + 3 \right)}}{\left(x + 3 \right)}


Respuesta:

(log(sin(x+3))+1)sinsin(x+3)(x+3)\left(\log{\left(\sin{\left(x + 3 \right)} \right)} + 1\right) \sin^{\sin{\left(x + 3 \right)}}{\left(x + 3 \right)}

Gráfica
02468-8-6-4-2-1010-1010
Segunda derivada [src]
            /                                2                                                \
 sin(3 + x) |/sin(3 + x)                    \    sin(3 + x)                       2*cos(3 + x)|
x          *||---------- + cos(3 + x)*log(x)|  - ---------- - log(x)*sin(3 + x) + ------------|
            |\    x                         /         2                                x      |
            \                                        x                                        /
xsin(x+3)((log(x)cos(x+3)+sin(x+3)x)2log(x)sin(x+3)+2cos(x+3)xsin(x+3)x2)x^{\sin{\left(x + 3 \right)}} \left(\left(\log{\left(x \right)} \cos{\left(x + 3 \right)} + \frac{\sin{\left(x + 3 \right)}}{x}\right)^{2} - \log{\left(x \right)} \sin{\left(x + 3 \right)} + \frac{2 \cos{\left(x + 3 \right)}}{x} - \frac{\sin{\left(x + 3 \right)}}{x^{2}}\right)
Tercera derivada [src]
            /                                3                                                                                                                                                      \
 sin(3 + x) |/sin(3 + x)                    \                        3*sin(3 + x)   3*cos(3 + x)     /sin(3 + x)                    \ /sin(3 + x)                       2*cos(3 + x)\   2*sin(3 + x)|
x          *||---------- + cos(3 + x)*log(x)|  - cos(3 + x)*log(x) - ------------ - ------------ - 3*|---------- + cos(3 + x)*log(x)|*|---------- + log(x)*sin(3 + x) - ------------| + ------------|
            |\    x                         /                             x               2          \    x                         / |     2                                x      |         3     |
            \                                                                            x                                            \    x                                        /        x      /
xsin(x+3)((log(x)cos(x+3)+sin(x+3)x)33(log(x)cos(x+3)+sin(x+3)x)(log(x)sin(x+3)2cos(x+3)x+sin(x+3)x2)log(x)cos(x+3)3sin(x+3)x3cos(x+3)x2+2sin(x+3)x3)x^{\sin{\left(x + 3 \right)}} \left(\left(\log{\left(x \right)} \cos{\left(x + 3 \right)} + \frac{\sin{\left(x + 3 \right)}}{x}\right)^{3} - 3 \left(\log{\left(x \right)} \cos{\left(x + 3 \right)} + \frac{\sin{\left(x + 3 \right)}}{x}\right) \left(\log{\left(x \right)} \sin{\left(x + 3 \right)} - \frac{2 \cos{\left(x + 3 \right)}}{x} + \frac{\sin{\left(x + 3 \right)}}{x^{2}}\right) - \log{\left(x \right)} \cos{\left(x + 3 \right)} - \frac{3 \sin{\left(x + 3 \right)}}{x} - \frac{3 \cos{\left(x + 3 \right)}}{x^{2}} + \frac{2 \sin{\left(x + 3 \right)}}{x^{3}}\right)
Gráfico
Derivada de x^sin(x+3)