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Derivada de la función/ cos^3/ y=-cos/ sqrt(x)/ y=-cos^3(4x)-arcctgsqrt(x)

Derivada de y=-cos^3(4x)-arcctgsqrt(x)

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

Ha introducido [src] 
     3            / 2\    
- cos (4*x) - acot\x /*t*x
$$- x t \operatorname{acot}{\left(x^{2} \right)} - \cos^{3}{\left(4 x \right)}$$ 
-cos(4*x)^3 - acot(x^2)*t*x
Primera derivada [src] 
                                            2
        / 2\         2                 2*t*x 
- t*acot\x / + 12*cos (4*x)*sin(4*x) + ------
                                            4
                                       1 + x
$$\frac{2 t x^{2}}{x^{4} + 1} - t \operatorname{acot}{\left(x^{2} \right)} + 12 \sin{\left(4 x \right)} \cos^{2}{\left(4 x \right)}$$
Simplificar
Segunda derivada [src] 
  /                                              5          \
  |      3              2                   4*t*x     3*t*x |
2*|24*cos (4*x) - 48*sin (4*x)*cos(4*x) - --------- + ------|
  |                                               2        4|
  |                                       /     4\    1 + x |
  \                                       \1 + x /          /
$$2 \left(- \frac{4 t x^{5}}{\left(x^{4} + 1\right)^{2}} + \frac{3 t x}{x^{4} + 1} - 48 \sin^{2}{\left(4 x \right)} \cos{\left(4 x \right)} + 24 \cos^{3}{\left(4 x \right)}\right)$$
Simplificar
Tercera derivada [src] 
  /                                                         4           8 \
  |       3               2                  3*t      32*t*x      32*t*x  |
2*|192*sin (4*x) - 672*cos (4*x)*sin(4*x) + ------ - --------- + ---------|
  |                                              4           2           3|
  |                                         1 + x    /     4\    /     4\ |
  \                                                  \1 + x /    \1 + x / /
$$2 \left(\frac{32 t x^{8}}{\left(x^{4} + 1\right)^{3}} - \frac{32 t x^{4}}{\left(x^{4} + 1\right)^{2}} + \frac{3 t}{x^{4} + 1} + 192 \sin^{3}{\left(4 x \right)} - 672 \sin{\left(4 x \right)} \cos^{2}{\left(4 x \right)}\right)$$
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