Sr Examen

Otras calculadoras


(sin(x))^(cos(x))

Derivada de (sin(x))^(cos(x))

Función f() - derivada -er orden en el punto
v

Gráfico:

interior superior

Definida a trozos:

Solución

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

    Perola derivada

    (log(cos(x))+1)coscos(x)(x)\left(\log{\left(\cos{\left(x \right)} \right)} + 1\right) \cos^{\cos{\left(x \right)}}{\left(x \right)}


Respuesta:

(log(cos(x))+1)coscos(x)(x)\left(\log{\left(\cos{\left(x \right)} \right)} + 1\right) \cos^{\cos{\left(x \right)}}{\left(x \right)}

Gráfica
02468-8-6-4-2-1010010000
Primera derivada [src]
             /   2                        \
   cos(x)    |cos (x)                     |
sin      (x)*|------- - log(sin(x))*sin(x)|
             \ sin(x)                     /
(log(sin(x))sin(x)+cos2(x)sin(x))sincos(x)(x)\left(- \log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)} + \frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)}}\right) \sin^{\cos{\left(x \right)}}{\left(x \right)}
Segunda derivada [src]
             /                              2                                     \
             |/                        2   \    /       2                 \       |
   cos(x)    ||                     cos (x)|    |    cos (x)              |       |
sin      (x)*||log(sin(x))*sin(x) - -------|  - |3 + ------- + log(sin(x))|*cos(x)|
             |\                      sin(x)/    |       2                 |       |
             \                                  \    sin (x)              /       /
((log(sin(x))sin(x)cos2(x)sin(x))2(log(sin(x))+3+cos2(x)sin2(x))cos(x))sincos(x)(x)\left(\left(\log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)} - \frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)}}\right)^{2} - \left(\log{\left(\sin{\left(x \right)} \right)} + 3 + \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \cos{\left(x \right)}\right) \sin^{\cos{\left(x \right)}}{\left(x \right)}
Tercera derivada [src]
             /                                3                                                                                                                              \
             |  /                        2   \                                         2           4        /                        2   \ /       2                 \       |
   cos(x)    |  |                     cos (x)|                                    2*cos (x)   2*cos (x)     |                     cos (x)| |    cos (x)              |       |
sin      (x)*|- |log(sin(x))*sin(x) - -------|  + 3*sin(x) + log(sin(x))*sin(x) + --------- + --------- + 3*|log(sin(x))*sin(x) - -------|*|3 + ------- + log(sin(x))|*cos(x)|
             |  \                      sin(x)/                                      sin(x)        3         \                      sin(x)/ |       2                 |       |
             \                                                                                 sin (x)                                     \    sin (x)              /       /
((log(sin(x))sin(x)cos2(x)sin(x))3+3(log(sin(x))sin(x)cos2(x)sin(x))(log(sin(x))+3+cos2(x)sin2(x))cos(x)+log(sin(x))sin(x)+3sin(x)+2cos2(x)sin(x)+2cos4(x)sin3(x))sincos(x)(x)\left(- \left(\log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)} - \frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)}}\right)^{3} + 3 \left(\log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)} - \frac{\cos^{2}{\left(x \right)}}{\sin{\left(x \right)}}\right) \left(\log{\left(\sin{\left(x \right)} \right)} + 3 + \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \cos{\left(x \right)} + \log{\left(\sin{\left(x \right)} \right)} \sin{\left(x \right)} + 3 \sin{\left(x \right)} + \frac{2 \cos^{2}{\left(x \right)}}{\sin{\left(x \right)}} + \frac{2 \cos^{4}{\left(x \right)}}{\sin^{3}{\left(x \right)}}\right) \sin^{\cos{\left(x \right)}}{\left(x \right)}
Gráfico
Derivada de (sin(x))^(cos(x))