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y=(4x^3-6x)^ctg3x

Derivada de y=(4x^3-6x)^ctg3x

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

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Solución

Ha introducido [src]
            cot(3*x)
/   3      \        
\4*x  - 6*x/        
$$\left(4 x^{3} - 6 x\right)^{\cot{\left(3 x \right)}}$$
(4*x^3 - 6*x)^cot(3*x)
Solución detallada
  1. No logro encontrar los pasos en la búsqueda de esta derivada.

    Perola derivada


Respuesta:

Gráfica
Primera derivada [src]
            cot(3*x) /                                     /         2\         \
/   3      \         |/          2     \    /   3      \   \-6 + 12*x /*cot(3*x)|
\4*x  - 6*x/        *|\-3 - 3*cot (3*x)/*log\4*x  - 6*x/ + ---------------------|
                     |                                              3           |
                     \                                           4*x  - 6*x     /
$$\left(4 x^{3} - 6 x\right)^{\cot{\left(3 x \right)}} \left(\frac{\left(12 x^{2} - 6\right) \cot{\left(3 x \right)}}{4 x^{3} - 6 x} + \left(- 3 \cot^{2}{\left(3 x \right)} - 3\right) \log{\left(4 x^{3} - 6 x \right)}\right)$$
Segunda derivada [src]
                            /                                                                 2                                                                                                               2         \
                   cot(3*x) |  /                                         /        2\         \                                                                     /       2     \ /        2\     /        2\          |
  /    /        2\\         |  |  /       2     \    /    /        2\\   \-1 + 2*x /*cot(3*x)|    4*cot(3*x)     /       2     \             /    /        2\\   6*\1 + cot (3*x)/*\-1 + 2*x /   3*\-1 + 2*x / *cot(3*x)|
3*\2*x*\-3 + 2*x //        *|3*|- \1 + cot (3*x)/*log\2*x*\-3 + 2*x // + --------------------|  + ---------- + 6*\1 + cot (3*x)/*cot(3*x)*log\2*x*\-3 + 2*x // - ----------------------------- - -----------------------|
                            |  |                                              /        2\    |            2                                                                /        2\                             2    |
                            |  \                                            x*\-3 + 2*x /    /    -3 + 2*x                                                               x*\-3 + 2*x /                2 /        2\     |
                            \                                                                                                                                                                        x *\-3 + 2*x /     /
$$3 \left(2 x \left(2 x^{2} - 3\right)\right)^{\cot{\left(3 x \right)}} \left(3 \left(- \left(\cot^{2}{\left(3 x \right)} + 1\right) \log{\left(2 x \left(2 x^{2} - 3\right) \right)} + \frac{\left(2 x^{2} - 1\right) \cot{\left(3 x \right)}}{x \left(2 x^{2} - 3\right)}\right)^{2} + 6 \left(\cot^{2}{\left(3 x \right)} + 1\right) \log{\left(2 x \left(2 x^{2} - 3\right) \right)} \cot{\left(3 x \right)} + \frac{4 \cot{\left(3 x \right)}}{2 x^{2} - 3} - \frac{6 \left(2 x^{2} - 1\right) \left(\cot^{2}{\left(3 x \right)} + 1\right)}{x \left(2 x^{2} - 3\right)} - \frac{3 \left(2 x^{2} - 1\right)^{2} \cot{\left(3 x \right)}}{x^{2} \left(2 x^{2} - 3\right)^{2}}\right)$$
Tercera derivada [src]
                            /                                                                 3                                                                                                                                     /                                                                                                            2         \                                                                                                               3                          2                                                          \
                   cot(3*x) |  /                                         /        2\         \       /       2     \                     2                          /                                         /        2\         \ |                                                                 /       2     \ /        2\     /        2\          |                                                                          /        2\               /        2\                /        2\  /       2     \      /       2     \ /        2\         |
  /    /        2\\         |  |  /       2     \    /    /        2\\   \-1 + 2*x /*cot(3*x)|    36*\1 + cot (3*x)/      /       2     \     /    /        2\\     |  /       2     \    /    /        2\\   \-1 + 2*x /*cot(3*x)| |4*cot(3*x)     /       2     \             /    /        2\\   6*\1 + cot (3*x)/*\-1 + 2*x /   3*\-1 + 2*x / *cot(3*x)|         2      /       2     \    /    /        2\\     4*cot(3*x)    36*\-1 + 2*x /*cot(3*x)   18*\-1 + 2*x / *cot(3*x)   27*\-1 + 2*x / *\1 + cot (3*x)/   54*\1 + cot (3*x)/*\-1 + 2*x /*cot(3*x)|
3*\2*x*\-3 + 2*x //        *|9*|- \1 + cot (3*x)/*log\2*x*\-3 + 2*x // + --------------------|  - ------------------ - 18*\1 + cot (3*x)/ *log\2*x*\-3 + 2*x // + 9*|- \1 + cot (3*x)/*log\2*x*\-3 + 2*x // + --------------------|*|---------- + 6*\1 + cot (3*x)/*cot(3*x)*log\2*x*\-3 + 2*x // - ----------------------------- - -----------------------| - 36*cot (3*x)*\1 + cot (3*x)/*log\2*x*\-3 + 2*x // + ------------- - ----------------------- + ------------------------ + ------------------------------- + ---------------------------------------|
                            |  |                                              /        2\    |                2                                                     |                                              /        2\    | |        2                                                                /        2\                             2    |                                                         /        2\                     2                         3                              2                          /        2\             |
                            |  \                                            x*\-3 + 2*x /    /        -3 + 2*x                                                      \                                            x*\-3 + 2*x /    / |-3 + 2*x                                                               x*\-3 + 2*x /                2 /        2\     |                                                       x*\-3 + 2*x /          /        2\             3 /        2\                  2 /        2\                         x*\-3 + 2*x /             |
                            \                                                                                                                                                                                                       \                                                                                                   x *\-3 + 2*x /     /                                                                            x*\-3 + 2*x /            x *\-3 + 2*x /                 x *\-3 + 2*x /                                                   /
$$3 \left(2 x \left(2 x^{2} - 3\right)\right)^{\cot{\left(3 x \right)}} \left(9 \left(- \left(\cot^{2}{\left(3 x \right)} + 1\right) \log{\left(2 x \left(2 x^{2} - 3\right) \right)} + \frac{\left(2 x^{2} - 1\right) \cot{\left(3 x \right)}}{x \left(2 x^{2} - 3\right)}\right)^{3} + 9 \left(- \left(\cot^{2}{\left(3 x \right)} + 1\right) \log{\left(2 x \left(2 x^{2} - 3\right) \right)} + \frac{\left(2 x^{2} - 1\right) \cot{\left(3 x \right)}}{x \left(2 x^{2} - 3\right)}\right) \left(6 \left(\cot^{2}{\left(3 x \right)} + 1\right) \log{\left(2 x \left(2 x^{2} - 3\right) \right)} \cot{\left(3 x \right)} + \frac{4 \cot{\left(3 x \right)}}{2 x^{2} - 3} - \frac{6 \left(2 x^{2} - 1\right) \left(\cot^{2}{\left(3 x \right)} + 1\right)}{x \left(2 x^{2} - 3\right)} - \frac{3 \left(2 x^{2} - 1\right)^{2} \cot{\left(3 x \right)}}{x^{2} \left(2 x^{2} - 3\right)^{2}}\right) - 18 \left(\cot^{2}{\left(3 x \right)} + 1\right)^{2} \log{\left(2 x \left(2 x^{2} - 3\right) \right)} - 36 \left(\cot^{2}{\left(3 x \right)} + 1\right) \log{\left(2 x \left(2 x^{2} - 3\right) \right)} \cot^{2}{\left(3 x \right)} - \frac{36 \left(\cot^{2}{\left(3 x \right)} + 1\right)}{2 x^{2} - 3} + \frac{54 \left(2 x^{2} - 1\right) \left(\cot^{2}{\left(3 x \right)} + 1\right) \cot{\left(3 x \right)}}{x \left(2 x^{2} - 3\right)} + \frac{4 \cot{\left(3 x \right)}}{x \left(2 x^{2} - 3\right)} - \frac{36 \left(2 x^{2} - 1\right) \cot{\left(3 x \right)}}{x \left(2 x^{2} - 3\right)^{2}} + \frac{27 \left(2 x^{2} - 1\right)^{2} \left(\cot^{2}{\left(3 x \right)} + 1\right)}{x^{2} \left(2 x^{2} - 3\right)^{2}} + \frac{18 \left(2 x^{2} - 1\right)^{3} \cot{\left(3 x \right)}}{x^{3} \left(2 x^{2} - 3\right)^{3}}\right)$$
Gráfico
Derivada de y=(4x^3-6x)^ctg3x