Sr Examen

Derivada de y=2cosxarctgx

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
2*cos(x)*atan(x)
2cos(x)atan(x)2 \cos{\left(x \right)} \operatorname{atan}{\left(x \right)}
(2*cos(x))*atan(x)
Gráfica
02468-8-6-4-2-10105-5
Primera derivada [src]
                    2*cos(x)
-2*atan(x)*sin(x) + --------
                          2 
                     1 + x  
2sin(x)atan(x)+2cos(x)x2+1- 2 \sin{\left(x \right)} \operatorname{atan}{\left(x \right)} + \frac{2 \cos{\left(x \right)}}{x^{2} + 1}
Segunda derivada [src]
   /                 2*sin(x)   2*x*cos(x)\
-2*|atan(x)*cos(x) + -------- + ----------|
   |                       2            2 |
   |                  1 + x     /     2\  |
   \                            \1 + x /  /
2(2xcos(x)(x2+1)2+cos(x)atan(x)+2sin(x)x2+1)- 2 \left(\frac{2 x \cos{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \cos{\left(x \right)} \operatorname{atan}{\left(x \right)} + \frac{2 \sin{\left(x \right)}}{x^{2} + 1}\right)
Tercera derivada [src]
  /                              /         2 \                    \
  |                              |      4*x  |                    |
  |                            2*|-1 + ------|*cos(x)             |
  |                              |          2|                    |
  |                 3*cos(x)     \     1 + x /          6*x*sin(x)|
2*|atan(x)*sin(x) - -------- + ---------------------- + ----------|
  |                       2                  2                  2 |
  |                  1 + x           /     2\           /     2\  |
  \                                  \1 + x /           \1 + x /  /
2(6xsin(x)(x2+1)2+sin(x)atan(x)3cos(x)x2+1+2(4x2x2+11)cos(x)(x2+1)2)2 \left(\frac{6 x \sin{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \sin{\left(x \right)} \operatorname{atan}{\left(x \right)} - \frac{3 \cos{\left(x \right)}}{x^{2} + 1} + \frac{2 \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=2cosxarctgx