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Derivada de:
Derivada de 5^10
Derivada de i*n*sin(x)
Derivada de √2x
Derivada de 3^-x
Expresiones idénticas
y=(sqrt(3x+ uno))^sin5x
y es igual a ( raíz cuadrada de (3x más 1)) en el grado seno de 5x
y es igual a ( raíz cuadrada de (3x más uno)) en el grado seno de 5x
y=(√(3x+1))^sin5x
y=(sqrt(3x+1))sin5x
y=sqrt3x+1sin5x
y=sqrt3x+1^sin5x
Expresiones semejantes
y=(sqrt(3x-1))^sin5x
Expresiones con funciones
Raíz cuadrada sqrt
sqrt(x)+1/x
sqrt(x^4-3*x)
sqrt((x)^2+1)*cos(6*x)
sqrt(x)+1/(sqrt(x))
sqrt(x)/(4+x)

Derivada de la función/ sin5x/ sqrt(3x+1)/ y=(sqrt(3x+1))^sin5x

Derivada de y=(sqrt(3x+1))^sin5x

Solución

Ha introducido [src]

           sin(5*x)
  _________        
\/ 3*x + 1

\left(\sqrt{3 x + 1}\right)^{\sin{\left(5 x \right)}}

(sqrt(3*x + 1))^sin(5*x)

Solución detallada

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

Perola derivada

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

Respuesta:

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

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

         sin(5*x)                                            
         --------                                            
            2     /              /  _________\    3*sin(5*x)\
(3*x + 1)        *|5*cos(5*x)*log\\/ 3*x + 1 / + -----------|
                  \                              2*(3*x + 1)/

\left(3 x + 1\right)^{\frac{\sin{\left(5 x \right)}}{2}} \left(5 \log{\left(\sqrt{3 x + 1} \right)} \cos{\left(5 x \right)} + \frac{3 \sin{\left(5 x \right)}}{2 \left(3 x + 1\right)}\right)

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Segunda derivada [src]

         sin(5*x) /                                                              /3*sin(5*x)                          \ /3*sin(5*x)                  /  _________\\\
         -------- |                                                              |---------- + 5*cos(5*x)*log(1 + 3*x)|*|---------- + 10*cos(5*x)*log\\/ 1 + 3*x /||
            2     |        /  _________\            15*cos(5*x)    9*sin(5*x)    \ 1 + 3*x                            / \ 1 + 3*x                                 /|
(1 + 3*x)        *|- 25*log\\/ 1 + 3*x /*sin(5*x) + ----------- - ------------ + ----------------------------------------------------------------------------------|
                  |                                   1 + 3*x                2                                           4                                         |
                  \                                               2*(1 + 3*x)                                                                                      /

\left(3 x + 1\right)^{\frac{\sin{\left(5 x \right)}}{2}} \left(\frac{\left(10 \log{\left(\sqrt{3 x + 1} \right)} \cos{\left(5 x \right)} + \frac{3 \sin{\left(5 x \right)}}{3 x + 1}\right) \left(5 \log{\left(3 x + 1 \right)} \cos{\left(5 x \right)} + \frac{3 \sin{\left(5 x \right)}}{3 x + 1}\right)}{4} - 25 \log{\left(\sqrt{3 x + 1} \right)} \sin{\left(5 x \right)} + \frac{15 \cos{\left(5 x \right)}}{3 x + 1} - \frac{9 \sin{\left(5 x \right)}}{2 \left(3 x + 1\right)^{2}}\right)

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Tercera derivada [src]

                  /                                                                              /3*sin(5*x)                          \ /  30*cos(5*x)   9*sin(5*x)         /  _________\         \   /3*sin(5*x)                  /  _________\\ /  30*cos(5*x)   9*sin(5*x)                           \                                         2                                            \
         sin(5*x) |                                                                              |---------- + 5*cos(5*x)*log(1 + 3*x)|*|- ----------- + ---------- + 50*log\\/ 1 + 3*x /*sin(5*x)|   |---------- + 10*cos(5*x)*log\\/ 1 + 3*x /|*|- ----------- + ---------- + 25*log(1 + 3*x)*sin(5*x)|   /3*sin(5*x)                          \  /3*sin(5*x)                  /  _________\\|
         -------- |                                                                              \ 1 + 3*x                            / |    1 + 3*x              2                               |   \ 1 + 3*x                                 / |    1 + 3*x              2                           |   |---------- + 5*cos(5*x)*log(1 + 3*x)| *|---------- + 10*cos(5*x)*log\\/ 1 + 3*x /||
            2     |                  /  _________\   27*sin(5*x)   225*sin(5*x)   135*cos(5*x)                                          \                (1 + 3*x)                                /                                               \                (1 + 3*x)                            /   \ 1 + 3*x                            /  \ 1 + 3*x                                 /|
(1 + 3*x)        *|- 125*cos(5*x)*log\\/ 1 + 3*x / + ----------- - ------------ - ------------ - -------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------- + -----------------------------------------------------------------------------------|
                  |                                            3   2*(1 + 3*x)               2                                                   2                                                                                                     4                                                                                             8                                         |
                  \                                   (1 + 3*x)                   2*(1 + 3*x)                                                                                                                                                                                                                                                                                                  /

\left(3 x + 1\right)^{\frac{\sin{\left(5 x \right)}}{2}} \left(\frac{\left(10 \log{\left(\sqrt{3 x + 1} \right)} \cos{\left(5 x \right)} + \frac{3 \sin{\left(5 x \right)}}{3 x + 1}\right) \left(5 \log{\left(3 x + 1 \right)} \cos{\left(5 x \right)} + \frac{3 \sin{\left(5 x \right)}}{3 x + 1}\right)^{2}}{8} - \frac{\left(10 \log{\left(\sqrt{3 x + 1} \right)} \cos{\left(5 x \right)} + \frac{3 \sin{\left(5 x \right)}}{3 x + 1}\right) \left(25 \log{\left(3 x + 1 \right)} \sin{\left(5 x \right)} - \frac{30 \cos{\left(5 x \right)}}{3 x + 1} + \frac{9 \sin{\left(5 x \right)}}{\left(3 x + 1\right)^{2}}\right)}{4} - \frac{\left(5 \log{\left(3 x + 1 \right)} \cos{\left(5 x \right)} + \frac{3 \sin{\left(5 x \right)}}{3 x + 1}\right) \left(50 \log{\left(\sqrt{3 x + 1} \right)} \sin{\left(5 x \right)} - \frac{30 \cos{\left(5 x \right)}}{3 x + 1} + \frac{9 \sin{\left(5 x \right)}}{\left(3 x + 1\right)^{2}}\right)}{2} - 125 \log{\left(\sqrt{3 x + 1} \right)} \cos{\left(5 x \right)} - \frac{225 \sin{\left(5 x \right)}}{2 \left(3 x + 1\right)} - \frac{135 \cos{\left(5 x \right)}}{2 \left(3 x + 1\right)^{2}} + \frac{27 \sin{\left(5 x \right)}}{\left(3 x + 1\right)^{3}}\right)

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Gráfico

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Derivada de y=(sqrt(3x+1))^sin5x

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