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y=arctgx/2*cosx3

Derivada de y=arctgx/2*cosx3

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

Ha introducido [src]
atan(x)         
-------*cos(x)*3
   2            
$$3 \frac{\operatorname{atan}{\left(x \right)}}{2} \cos{\left(x \right)}$$
((atan(x)/2)*cos(x))*3
Gráfica
Primera derivada [src]
  3*atan(x)*sin(x)    3*cos(x) 
- ---------------- + ----------
         2             /     2\
                     2*\1 + x /
$$- \frac{3 \sin{\left(x \right)} \operatorname{atan}{\left(x \right)}}{2} + \frac{3 \cos{\left(x \right)}}{2 \left(x^{2} + 1\right)}$$
Segunda derivada [src]
   /sin(x)   atan(x)*cos(x)    x*cos(x)\
-3*|------ + -------------- + ---------|
   |     2         2                  2|
   |1 + x                     /     2\ |
   \                          \1 + x / /
$$- 3 \left(\frac{x \cos{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{\cos{\left(x \right)} \operatorname{atan}{\left(x \right)}}{2} + \frac{\sin{\left(x \right)}}{x^{2} + 1}\right)$$
Tercera derivada [src]
  /                              /         2 \                    \
  |                              |      4*x  |                    |
  |                              |-1 + ------|*cos(x)             |
  |                              |          2|                    |
  |atan(x)*sin(x)    3*cos(x)    \     1 + x /          3*x*sin(x)|
3*|-------------- - ---------- + -------------------- + ----------|
  |      2            /     2\                2                 2 |
  |                 2*\1 + x /        /     2\          /     2\  |
  \                                   \1 + x /          \1 + x /  /
$$3 \left(\frac{3 x \sin{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{\sin{\left(x \right)} \operatorname{atan}{\left(x \right)}}{2} - \frac{3 \cos{\left(x \right)}}{2 \left(x^{2} + 1\right)} + \frac{\left(\frac{4 x^{2}}{x^{2} + 1} - 1\right) \cos{\left(x \right)}}{\left(x^{2} + 1\right)^{2}}\right)$$
Gráfico
Derivada de y=arctgx/2*cosx3