Sr Examen

Derivada de y=arcctgx/2-arctg6x2

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

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Solución

Ha introducido [src]
acot(x)              
------- - atan(6*x)*2
   2                 
acot(x)22atan(6x)\frac{\operatorname{acot}{\left(x \right)}}{2} - 2 \operatorname{atan}{\left(6 x \right)}
acot(x)/2 - atan(6*x)*2
Gráfica
02468-8-6-4-2-1010-1010
Primera derivada [src]
      12          1     
- --------- - ----------
          2     /     2\
  1 + 36*x    2*\1 + x /
1236x2+112(x2+1)- \frac{12}{36 x^{2} + 1} - \frac{1}{2 \left(x^{2} + 1\right)}
Segunda derivada [src]
  /    1           864     \
x*|--------- + ------------|
  |        2              2|
  |/     2\    /        2\ |
  \\1 + x /    \1 + 36*x / /
x(864(36x2+1)2+1(x2+1)2)x \left(\frac{864}{\left(36 x^{2} + 1\right)^{2}} + \frac{1}{\left(x^{2} + 1\right)^{2}}\right)
Tercera derivada [src]
                                    2           2  
    1           864         124416*x         4*x   
--------- + ------------ - ------------ - ---------
        2              2              3           3
/     2\    /        2\    /        2\    /     2\ 
\1 + x /    \1 + 36*x /    \1 + 36*x /    \1 + x / 
124416x2(36x2+1)34x2(x2+1)3+864(36x2+1)2+1(x2+1)2- \frac{124416 x^{2}}{\left(36 x^{2} + 1\right)^{3}} - \frac{4 x^{2}}{\left(x^{2} + 1\right)^{3}} + \frac{864}{\left(36 x^{2} + 1\right)^{2}} + \frac{1}{\left(x^{2} + 1\right)^{2}}
Gráfico
Derivada de y=arcctgx/2-arctg6x2