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y=(sinx^ dos)^sin7x
y es igual a ( seno de x al cuadrado ) en el grado seno de 7x
y es igual a ( seno de x en el grado dos) en el grado seno de 7x
y=(sinx2)sin7x
y=sinx2sin7x
y=(sinx²)^sin7x
y=(sinx en el grado 2) en el grado sin7x
y=sinx^2^sin7x
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sinx
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Derivada de la función/ sin7x/ sinx^2/ y=(sinx^2)^sin7x

Derivada de y=(sinx^2)^sin7x

Solución

Ha introducido [src]

       sin(7*x)
   2           
sin (x)

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

(sin(x)^2)^sin(7*x)

Solución detallada

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

Perola derivada

$\left(\log{\left(\sin{\left(7 x \right)} \right)} + 1\right) \sin^{\sin{\left(7 x \right)}}{\left(7 x \right)}$

Respuesta:

$\left(\log{\left(\sin{\left(7 x \right)} \right)} + 1\right) \sin^{\sin{\left(7 x \right)}}{\left(7 x \right)}$

Primera derivada [src]

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

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

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Segunda derivada [src]

                   /                                                                                                                                                          2                                 \
        2*sin(7*x) |                    /   2   \              /              /   2   \   2*cos(x)*sin(7*x)\ /                           cos(x)*sign(sin(x))*sin(7*x)\   2*cos (x)*sin(7*x)   28*cos(x)*cos(7*x)|
|sin(x)|          *|-2*sin(7*x) - 49*log\sin (x)/*sin(7*x) + 2*|7*cos(7*x)*log\sin (x)/ + -----------------|*|7*cos(7*x)*log(|sin(x)|) + ----------------------------| - ------------------ + ------------------|
                   |                                           \                                sin(x)     / \                                     |sin(x)|          /           2                  sin(x)      |
                   \                                                                                                                                                          sin (x)                           /

\left(2 \left(7 \log{\left(\sin^{2}{\left(x \right)} \right)} \cos{\left(7 x \right)} + \frac{2 \sin{\left(7 x \right)} \cos{\left(x \right)}}{\sin{\left(x \right)}}\right) \left(7 \log{\left(\left|{\sin{\left(x \right)}}\right| \right)} \cos{\left(7 x \right)} + \frac{\sin{\left(7 x \right)} \cos{\left(x \right)} \operatorname{sign}{\left(\sin{\left(x \right)} \right)}}{\left|{\sin{\left(x \right)}}\right|}\right) - 49 \log{\left(\sin^{2}{\left(x \right)} \right)} \sin{\left(7 x \right)} - 2 \sin{\left(7 x \right)} + \frac{28 \cos{\left(x \right)} \cos{\left(7 x \right)}}{\sin{\left(x \right)}} - \frac{2 \sin{\left(7 x \right)} \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \left|{\sin{\left(x \right)}}\right|^{2 \sin{\left(7 x \right)}}

Simplificar

Tercera derivada [src]

                   /                                                                                                       /                                                                  2            \                                                   /                                                              2        2                                                           2                               \                                                              2                                                                             2                    3            \
        2*sin(7*x) |                               /   2   \     /                           cos(x)*sign(sin(x))*sin(7*x)\ |                   /   2   \            28*cos(x)*cos(7*x)   2*cos (x)*sin(7*x)|     /              /   2   \   2*cos(x)*sin(7*x)\ |                            sign(sin(x))*sin(x)*sin(7*x)   cos (x)*sign (sin(x))*sin(7*x)   14*cos(x)*cos(7*x)*sign(sin(x))   2*cos (x)*DiracDelta(sin(x))*sin(7*x)|     /                           cos(x)*sign(sin(x))*sin(7*x)\  /              /   2   \   2*cos(x)*sin(7*x)\   290*cos(x)*sin(7*x)   42*cos (x)*cos(7*x)   4*cos (x)*sin(7*x)|
|sin(x)|          *|-42*cos(7*x) - 343*cos(7*x)*log\sin (x)/ - 4*|7*cos(7*x)*log(|sin(x)|) + ----------------------------|*|2*sin(7*x) + 49*log\sin (x)/*sin(7*x) - ------------------ + ------------------| - 2*|7*cos(7*x)*log\sin (x)/ + -----------------|*|49*log(|sin(x)|)*sin(7*x) + ---------------------------- + ------------------------------ - ------------------------------- - -------------------------------------| + 4*|7*cos(7*x)*log(|sin(x)|) + ----------------------------| *|7*cos(7*x)*log\sin (x)/ + -----------------| - ------------------- - ------------------- + ------------------|
                   |                                             \                                     |sin(x)|          / |                                              sin(x)                 2         |     \                                sin(x)     / |                                      |sin(x)|                           2                              |sin(x)|                             |sin(x)|              |     \                                     |sin(x)|          /  \                                sin(x)     /          sin(x)                  2                    3         |
                   \                                                                                                       \                                                                  sin (x)      /                                                   \                                                                      sin (x)                                                                                      /                                                                                                                                            sin (x)              sin (x)      /

\left(4 \left(7 \log{\left(\sin^{2}{\left(x \right)} \right)} \cos{\left(7 x \right)} + \frac{2 \sin{\left(7 x \right)} \cos{\left(x \right)}}{\sin{\left(x \right)}}\right) \left(7 \log{\left(\left|{\sin{\left(x \right)}}\right| \right)} \cos{\left(7 x \right)} + \frac{\sin{\left(7 x \right)} \cos{\left(x \right)} \operatorname{sign}{\left(\sin{\left(x \right)} \right)}}{\left|{\sin{\left(x \right)}}\right|}\right)^{2} - 2 \left(7 \log{\left(\sin^{2}{\left(x \right)} \right)} \cos{\left(7 x \right)} + \frac{2 \sin{\left(7 x \right)} \cos{\left(x \right)}}{\sin{\left(x \right)}}\right) \left(49 \log{\left(\left|{\sin{\left(x \right)}}\right| \right)} \sin{\left(7 x \right)} + \frac{\sin{\left(x \right)} \sin{\left(7 x \right)} \operatorname{sign}{\left(\sin{\left(x \right)} \right)}}{\left|{\sin{\left(x \right)}}\right|} - \frac{2 \sin{\left(7 x \right)} \cos^{2}{\left(x \right)} \delta\left(\sin{\left(x \right)}\right)}{\left|{\sin{\left(x \right)}}\right|} - \frac{14 \cos{\left(x \right)} \cos{\left(7 x \right)} \operatorname{sign}{\left(\sin{\left(x \right)} \right)}}{\left|{\sin{\left(x \right)}}\right|} + \frac{\sin{\left(7 x \right)} \cos^{2}{\left(x \right)} \operatorname{sign}^{2}{\left(\sin{\left(x \right)} \right)}}{\sin^{2}{\left(x \right)}}\right) - 4 \left(7 \log{\left(\left|{\sin{\left(x \right)}}\right| \right)} \cos{\left(7 x \right)} + \frac{\sin{\left(7 x \right)} \cos{\left(x \right)} \operatorname{sign}{\left(\sin{\left(x \right)} \right)}}{\left|{\sin{\left(x \right)}}\right|}\right) \left(49 \log{\left(\sin^{2}{\left(x \right)} \right)} \sin{\left(7 x \right)} + 2 \sin{\left(7 x \right)} - \frac{28 \cos{\left(x \right)} \cos{\left(7 x \right)}}{\sin{\left(x \right)}} + \frac{2 \sin{\left(7 x \right)} \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) - 343 \log{\left(\sin^{2}{\left(x \right)} \right)} \cos{\left(7 x \right)} - 42 \cos{\left(7 x \right)} - \frac{290 \sin{\left(7 x \right)} \cos{\left(x \right)}}{\sin{\left(x \right)}} - \frac{42 \cos^{2}{\left(x \right)} \cos{\left(7 x \right)}}{\sin^{2}{\left(x \right)}} + \frac{4 \sin{\left(7 x \right)} \cos^{3}{\left(x \right)}}{\sin^{3}{\left(x \right)}}\right) \left|{\sin{\left(x \right)}}\right|^{2 \sin{\left(7 x \right)}}

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Derivada de y=(sinx^2)^sin7x

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Solución