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Derivada de:
Derivada de e^x*sin(x)
Derivada de 2*cos(3*x)
Derivada de 1/t
Derivada de x^(7/6)
Expresiones idénticas
y=sin7x^(√(3x+ dos))
y es igual a seno de 7x en el grado (√(3x más 2))
y es igual a seno de 7x en el grado (√(3x más dos))
y=sin7x(√(3x+2))
y=sin7x√3x+2
y=sin7x^√3x+2
Expresiones semejantes
y=sin7x^(√(3x-2))

Derivada de la función/ sin7x/ y=sin/ √(3x+2)/ y=sin7x^(√(3x+2))

Derivada de y=sin7x^(√(3x+2))

Solución

Ha introducido [src]

            _________
          \/ 3*x + 2 
(sin(7*x))

\sin^{\sqrt{3 x + 2}}{\left(7 x \right)}

sin(7*x)^(sqrt(3*x + 2))

Solución detallada

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

Perola derivada

$\left(3 x + 2\right)^{\frac{\sqrt{3 x + 2}}{2}} \left(\log{\left(\sqrt{3 x + 2} \right)} + 1\right)$
Simplificamos:

$\frac{\left(3 x + 2\right)^{\frac{\sqrt{3 x + 2}}{2}} \left(\log{\left(3 x + 2 \right)} + 2\right)}{2}$

Respuesta:

$\frac{\left(3 x + 2\right)^{\frac{\sqrt{3 x + 2}}{2}} \left(\log{\left(3 x + 2 \right)} + 2\right)}{2}$

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

            _________ /                      _________         \
          \/ 3*x + 2  |3*log(sin(7*x))   7*\/ 3*x + 2 *cos(7*x)|
(sin(7*x))           *|--------------- + ----------------------|
                      |     _________           sin(7*x)       |
                      \ 2*\/ 3*x + 2                           /

\left(\frac{7 \sqrt{3 x + 2} \cos{\left(7 x \right)}}{\sin{\left(7 x \right)}} + \frac{3 \log{\left(\sin{\left(7 x \right)} \right)}}{2 \sqrt{3 x + 2}}\right) \sin^{\sqrt{3 x + 2}}{\left(7 x \right)}

Simplificar

Segunda derivada [src]

                      /                                                              2                                                                    \
                      |                   /                       _________         \                                                                     |
                      |                   |3*log(sin(7*x))   14*\/ 2 + 3*x *cos(7*x)|                                                                     |
                      |                   |--------------- + -----------------------|                                                                     |
            _________ |                   |    _________             sin(7*x)       |                           _________    2                            |
          \/ 2 + 3*x  |       _________   \  \/ 2 + 3*x                             /    9*log(sin(7*x))   49*\/ 2 + 3*x *cos (7*x)       21*cos(7*x)     |
(sin(7*x))           *|- 49*\/ 2 + 3*x  + -------------------------------------------- - --------------- - ------------------------ + --------------------|
                      |                                        4                                     3/2             2                  _________         |
                      \                                                                   4*(2 + 3*x)             sin (7*x)           \/ 2 + 3*x *sin(7*x)/

\left(- 49 \sqrt{3 x + 2} - \frac{49 \sqrt{3 x + 2} \cos^{2}{\left(7 x \right)}}{\sin^{2}{\left(7 x \right)}} + \frac{\left(\frac{14 \sqrt{3 x + 2} \cos{\left(7 x \right)}}{\sin{\left(7 x \right)}} + \frac{3 \log{\left(\sin{\left(7 x \right)} \right)}}{\sqrt{3 x + 2}}\right)^{2}}{4} + \frac{21 \cos{\left(7 x \right)}}{\sqrt{3 x + 2} \sin{\left(7 x \right)}} - \frac{9 \log{\left(\sin{\left(7 x \right)} \right)}}{4 \left(3 x + 2\right)^{\frac{3}{2}}}\right) \sin^{\sqrt{3 x + 2}}{\left(7 x \right)}

Simplificar

Tercera derivada [src]

                      /                                                             3                                                                                                                                                                                                                                                                     \
                      |                  /                       _________         \      /                       _________         \ /                                                                 _________    2     \                                                                                                                              |
                      |                  |3*log(sin(7*x))   14*\/ 2 + 3*x *cos(7*x)|      |3*log(sin(7*x))   14*\/ 2 + 3*x *cos(7*x)| |      _________   9*log(sin(7*x))       84*cos(7*x)        196*\/ 2 + 3*x *cos (7*x)|                                                                                                                              |
                      |                  |--------------- + -----------------------|    3*|--------------- + -----------------------|*|196*\/ 2 + 3*x  + --------------- - -------------------- + -------------------------|                                                                                                                              |
            _________ |                  |    _________             sin(7*x)       |      |    _________             sin(7*x)       | |                             3/2      _________                       2             |                            _________    3              _________                        2                                    |
          \/ 2 + 3*x  |       441        \  \/ 2 + 3*x                             /      \  \/ 2 + 3*x                             / \                    (2 + 3*x)       \/ 2 + 3*x *sin(7*x)           sin (7*x)        /   81*log(sin(7*x))   686*\/ 2 + 3*x *cos (7*x)   686*\/ 2 + 3*x *cos(7*x)        441*cos (7*x)              189*cos(7*x)     |
(sin(7*x))           *|- ------------- + -------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------ + ---------------- + ------------------------- + ------------------------ - ----------------------- - -----------------------|
                      |      _________                        8                                                                                          8                                                                                 5/2               3                        sin(7*x)               _________    2                   3/2         |
                      \  2*\/ 2 + 3*x                                                                                                                                                                                           8*(2 + 3*x)               sin (7*x)                                      2*\/ 2 + 3*x *sin (7*x)   4*(2 + 3*x)   *sin(7*x)/

\left(\frac{686 \sqrt{3 x + 2} \cos{\left(7 x \right)}}{\sin{\left(7 x \right)}} + \frac{686 \sqrt{3 x + 2} \cos^{3}{\left(7 x \right)}}{\sin^{3}{\left(7 x \right)}} + \frac{\left(\frac{14 \sqrt{3 x + 2} \cos{\left(7 x \right)}}{\sin{\left(7 x \right)}} + \frac{3 \log{\left(\sin{\left(7 x \right)} \right)}}{\sqrt{3 x + 2}}\right)^{3}}{8} - \frac{3 \left(\frac{14 \sqrt{3 x + 2} \cos{\left(7 x \right)}}{\sin{\left(7 x \right)}} + \frac{3 \log{\left(\sin{\left(7 x \right)} \right)}}{\sqrt{3 x + 2}}\right) \left(196 \sqrt{3 x + 2} + \frac{196 \sqrt{3 x + 2} \cos^{2}{\left(7 x \right)}}{\sin^{2}{\left(7 x \right)}} - \frac{84 \cos{\left(7 x \right)}}{\sqrt{3 x + 2} \sin{\left(7 x \right)}} + \frac{9 \log{\left(\sin{\left(7 x \right)} \right)}}{\left(3 x + 2\right)^{\frac{3}{2}}}\right)}{8} - \frac{441}{2 \sqrt{3 x + 2}} - \frac{441 \cos^{2}{\left(7 x \right)}}{2 \sqrt{3 x + 2} \sin^{2}{\left(7 x \right)}} - \frac{189 \cos{\left(7 x \right)}}{4 \left(3 x + 2\right)^{\frac{3}{2}} \sin{\left(7 x \right)}} + \frac{81 \log{\left(\sin{\left(7 x \right)} \right)}}{8 \left(3 x + 2\right)^{\frac{5}{2}}}\right) \sin^{\sqrt{3 x + 2}}{\left(7 x \right)}

Simplificar

Gráfico

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Expresiones idénticas

Expresiones semejantes

Derivada de y=sin7x^(√(3x+2))

Gráfico:

Definida a trozos:

Solución