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y=tg(sqrtx)*arctg3x^5

Derivada de y=tg(sqrtx)*arctg3x^5

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

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Solución

Ha introducido [src]
   /  ___\     5     
tan\\/ x /*atan (3*x)
$$\tan{\left(\sqrt{x} \right)} \operatorname{atan}^{5}{\left(3 x \right)}$$
tan(sqrt(x))*atan(3*x)^5
Gráfica
Primera derivada [src]
    5      /       2/  ___\\          4         /  ___\
atan (3*x)*\1 + tan \\/ x //   15*atan (3*x)*tan\\/ x /
---------------------------- + ------------------------
              ___                             2        
          2*\/ x                       1 + 9*x         
$$\frac{15 \tan{\left(\sqrt{x} \right)} \operatorname{atan}^{4}{\left(3 x \right)}}{9 x^{2} + 1} + \frac{\left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right) \operatorname{atan}^{5}{\left(3 x \right)}}{2 \sqrt{x}}$$
Segunda derivada [src]
           /                                                                    /              /  ___\\                                 \
           |                                           2      /       2/  ___\\ |   1     2*tan\\/ x /|                                 |
           |                                       atan (3*x)*\1 + tan \\/ x //*|- ---- + ------------|                                 |
           |                             /  ___\                                |   3/2        x      |      /       2/  ___\\          |
    3      |  90*(-2 + 3*x*atan(3*x))*tan\\/ x /                                \  x                  /   15*\1 + tan \\/ x //*atan(3*x)|
atan (3*x)*|- ---------------------------------- + ---------------------------------------------------- + ------------------------------|
           |                       2                                        4                                      ___ /       2\       |
           |             /       2\                                                                              \/ x *\1 + 9*x /       |
           \             \1 + 9*x /                                                                                                     /
$$\left(\frac{\left(\frac{2 \tan{\left(\sqrt{x} \right)}}{x} - \frac{1}{x^{\frac{3}{2}}}\right) \left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right) \operatorname{atan}^{2}{\left(3 x \right)}}{4} - \frac{90 \left(3 x \operatorname{atan}{\left(3 x \right)} - 2\right) \tan{\left(\sqrt{x} \right)}}{\left(9 x^{2} + 1\right)^{2}} + \frac{15 \left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right) \operatorname{atan}{\left(3 x \right)}}{\sqrt{x} \left(9 x^{2} + 1\right)}\right) \operatorname{atan}^{3}{\left(3 x \right)}$$
Tercera derivada [src]
           /    /                                               2     2     \                                           /            /  ___\     /       2/  ___\\        2/  ___\\                                   /              /  ___\\                                                       \
           |    |      2           6       36*x*atan(3*x)   36*x *atan (3*x)|    /  ___\       3      /       2/  ___\\ | 3     6*tan\\/ x /   2*\1 + tan \\/ x //   4*tan \\/ x /|          2      /       2/  ___\\ |   1     2*tan\\/ x /|                                                       |
           |270*|- atan (3*x) + -------- - -------------- + ----------------|*tan\\/ x /   atan (3*x)*\1 + tan \\/ x //*|---- - ------------ + ------------------- + -------------|   45*atan (3*x)*\1 + tan \\/ x //*|- ---- + ------------|                                                       |
           |    |                      2             2                 2    |                                           | 5/2         2                 3/2                3/2    |                                   |   3/2        x      |       /       2/  ___\\                               |
    2      |    \               1 + 9*x       1 + 9*x           1 + 9*x     /                                           \x           x                 x                  x       /                                   \  x                  /   135*\1 + tan \\/ x //*(-2 + 3*x*atan(3*x))*atan(3*x)|
atan (3*x)*|---------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------- + ------------------------------------------------------- - ----------------------------------------------------|
           |                                          2                                                                               8                                                                       /       2\                                                         2                  |
           |                                /       2\                                                                                                                                                      4*\1 + 9*x /                                           ___ /       2\                   |
           \                                \1 + 9*x /                                                                                                                                                                                                           \/ x *\1 + 9*x /                   /
$$\left(\frac{\left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right) \left(- \frac{6 \tan{\left(\sqrt{x} \right)}}{x^{2}} + \frac{2 \left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right)}{x^{\frac{3}{2}}} + \frac{4 \tan^{2}{\left(\sqrt{x} \right)}}{x^{\frac{3}{2}}} + \frac{3}{x^{\frac{5}{2}}}\right) \operatorname{atan}^{3}{\left(3 x \right)}}{8} + \frac{45 \left(\frac{2 \tan{\left(\sqrt{x} \right)}}{x} - \frac{1}{x^{\frac{3}{2}}}\right) \left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right) \operatorname{atan}^{2}{\left(3 x \right)}}{4 \left(9 x^{2} + 1\right)} + \frac{270 \left(\frac{36 x^{2} \operatorname{atan}^{2}{\left(3 x \right)}}{9 x^{2} + 1} - \frac{36 x \operatorname{atan}{\left(3 x \right)}}{9 x^{2} + 1} - \operatorname{atan}^{2}{\left(3 x \right)} + \frac{6}{9 x^{2} + 1}\right) \tan{\left(\sqrt{x} \right)}}{\left(9 x^{2} + 1\right)^{2}} - \frac{135 \left(3 x \operatorname{atan}{\left(3 x \right)} - 2\right) \left(\tan^{2}{\left(\sqrt{x} \right)} + 1\right) \operatorname{atan}{\left(3 x \right)}}{\sqrt{x} \left(9 x^{2} + 1\right)^{2}}\right) \operatorname{atan}^{2}{\left(3 x \right)}$$
Gráfico
Derivada de y=tg(sqrtx)*arctg3x^5