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y=(xarctyx^3)+sin^2(5/x)

Derivada de y=(xarctyx^3)+sin^2(5/x)

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

Ha introducido [src]
      3         2/5\
x*atan (x) + sin |-|
                 \x/
$$x \operatorname{atan}^{3}{\left(x \right)} + \sin^{2}{\left(\frac{5}{x} \right)}$$
x*atan(x)^3 + sin(5/x)^2
Gráfica
Primera derivada [src]
                 /5\    /5\               
           10*cos|-|*sin|-|           2   
    3            \x/    \x/   3*x*atan (x)
atan (x) - ---------------- + ------------
                   2                  2   
                  x              1 + x    
$$\frac{3 x \operatorname{atan}^{2}{\left(x \right)}}{x^{2} + 1} + \operatorname{atan}^{3}{\left(x \right)} - \frac{10 \sin{\left(\frac{5}{x} \right)} \cos{\left(\frac{5}{x} \right)}}{x^{2}}$$
Segunda derivada [src]
  /        2/5\                      2/5\                                       /5\    /5\\
  |  25*sin |-|         2      25*cos |-|      2     2                    10*cos|-|*sin|-||
  |         \x/   3*atan (x)          \x/   3*x *atan (x)   3*x*atan(x)         \x/    \x/|
2*|- ---------- + ---------- + ---------- - ------------- + ----------- + ----------------|
  |       4              2          4                 2              2            3       |
  |      x          1 + x          x          /     2\       /     2\            x        |
  \                                           \1 + x /       \1 + x /                     /
$$2 \left(- \frac{3 x^{2} \operatorname{atan}^{2}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{3 x \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{3 \operatorname{atan}^{2}{\left(x \right)}}{x^{2} + 1} + \frac{10 \sin{\left(\frac{5}{x} \right)} \cos{\left(\frac{5}{x} \right)}}{x^{3}} - \frac{25 \sin^{2}{\left(\frac{5}{x} \right)}}{x^{4}} + \frac{25 \cos^{2}{\left(\frac{5}{x} \right)}}{x^{4}}\right)$$
Tercera derivada [src]
  /         2/5\                                  2/5\         /5\    /5\                                                           /5\    /5\\
  |  150*cos |-|                           150*sin |-|   30*cos|-|*sin|-|       2                    2          3     2      500*cos|-|*sin|-||
  |          \x/      3*x      9*atan(x)           \x/         \x/    \x/   18*x *atan(x)   12*x*atan (x)   12*x *atan (x)          \x/    \x/|
2*|- ----------- + --------- + --------- + ----------- - ---------------- - ------------- - ------------- + -------------- + -----------------|
  |        5               3           2         5               4                    3               2               3               6       |
  |       x        /     2\    /     2\         x               x             /     2\        /     2\        /     2\               x        |
  \                \1 + x /    \1 + x /                                       \1 + x /        \1 + x /        \1 + x /                        /
$$2 \left(\frac{12 x^{3} \operatorname{atan}^{2}{\left(x \right)}}{\left(x^{2} + 1\right)^{3}} - \frac{18 x^{2} \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{3}} - \frac{12 x \operatorname{atan}^{2}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{3 x}{\left(x^{2} + 1\right)^{3}} + \frac{9 \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{30 \sin{\left(\frac{5}{x} \right)} \cos{\left(\frac{5}{x} \right)}}{x^{4}} + \frac{150 \sin^{2}{\left(\frac{5}{x} \right)}}{x^{5}} - \frac{150 \cos^{2}{\left(\frac{5}{x} \right)}}{x^{5}} + \frac{500 \sin{\left(\frac{5}{x} \right)} \cos{\left(\frac{5}{x} \right)}}{x^{6}}\right)$$
Gráfico
Derivada de y=(xarctyx^3)+sin^2(5/x)