Sr Examen

Otras calculadoras

y=(4x^2-5x-3)^2*arctg^2x
Derivada de la función/ ctg^2/ x^2-5/ arctg/ tg^2x/ y=(4x^2-5x-3)^2*arctg^2x

Derivada de y=(4x^2-5x-3)^2*arctg^2x

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
                2         
/   2          \      2   
\4*x  - 5*x - 3/ *atan (x)
((4x2−5x)−3)2atan⁡2(x)\left(\left(4 x^{2} - 5 x\right) - 3\right)^{2} \operatorname{atan}^{2}{\left(x \right)} 
(4*x^2 - 5*x - 3)^2*atan(x)^2
Gráfica
02468-8-6-4-2-1010-500000500000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
                                                           2        
                                           /   2          \         
    2                 /   2          \   2*\4*x  - 5*x - 3/ *atan(x)
atan (x)*(-10 + 16*x)*\4*x  - 5*x - 3/ + ---------------------------
                                                         2          
                                                    1 + x
(16x−10)((4x2−5x)−3)atan⁡2(x)+2((4x2−5x)−3)2atan⁡(x)x2+1\left(16 x - 10\right) \left(\left(4 x^{2} - 5 x\right) - 3\right) \operatorname{atan}^{2}{\left(x \right)} + \frac{2 \left(\left(4 x^{2} - 5 x\right) - 3\right)^{2} \operatorname{atan}{\left(x \right)}}{x^{2} + 1}
Simplificar
Segunda derivada [src] 
  /                                                                2                                                           \
  |                                                /       2      \                                    /       2      \        |
  |    2    /                2                 \   \3 - 4*x  + 5*x/ *(-1 + 2*x*atan(x))   4*(-5 + 8*x)*\3 - 4*x  + 5*x/*atan(x)|
2*|atan (x)*\-24 + (-5 + 8*x)  + 8*x*(-5 + 4*x)/ - ------------------------------------ - -------------------------------------|
  |                                                                     2                                      2               |
  |                                                             /     2\                                  1 + x                |
  \                                                             \1 + x /                                                       /
2(−4(8x−5)(−4x2+5x+3)atan⁡(x)x2+1+(8x(4x−5)+(8x−5)2−24)atan⁡2(x)−(2xatan⁡(x)−1)(−4x2+5x+3)2(x2+1)2)2 \left(- \frac{4 \left(8 x - 5\right) \left(- 4 x^{2} + 5 x + 3\right) \operatorname{atan}{\left(x \right)}}{x^{2} + 1} + \left(8 x \left(4 x - 5\right) + \left(8 x - 5\right)^{2} - 24\right) \operatorname{atan}^{2}{\left(x \right)} - \frac{\left(2 x \operatorname{atan}{\left(x \right)} - 1\right) \left(- 4 x^{2} + 5 x + 3\right)^{2}}{\left(x^{2} + 1\right)^{2}}\right)
Simplificar
Tercera derivada [src] 
  /                                         2 /            2                  \                                                                                                    \
  |                         /       2      \  | 3*x     4*x *atan(x)          |                                                                                                    |
  |                         \3 - 4*x  + 5*x/ *|------ - ------------ + atan(x)|                                                                                                    |
  |                                           |     2           2             |     /                2                 \                                           /       2      \|
  |       2                                   \1 + x       1 + x              /   3*\-24 + (-5 + 8*x)  + 8*x*(-5 + 4*x)/*atan(x)   3*(-1 + 2*x*atan(x))*(-5 + 8*x)*\3 - 4*x  + 5*x/|
4*|12*atan (x)*(-5 + 8*x) - --------------------------------------------------- + ---------------------------------------------- + ------------------------------------------------|
  |                                                      2                                                 2                                                  2                    |
  |                                              /     2\                                             1 + x                                           /     2\                     |
  \                                              \1 + x /                                                                                             \1 + x /                     /
4(12(8x−5)atan⁡2(x)+3(8x−5)(2xatan⁡(x)−1)(−4x2+5x+3)(x2+1)2+3(8x(4x−5)+(8x−5)2−24)atan⁡(x)x2+1−(−4x2+5x+3)2(−4x2atan⁡(x)x2+1+3xx2+1+atan⁡(x))(x2+1)2)4 \left(12 \left(8 x - 5\right) \operatorname{atan}^{2}{\left(x \right)} + \frac{3 \left(8 x - 5\right) \left(2 x \operatorname{atan}{\left(x \right)} - 1\right) \left(- 4 x^{2} + 5 x + 3\right)}{\left(x^{2} + 1\right)^{2}} + \frac{3 \left(8 x \left(4 x - 5\right) + \left(8 x - 5\right)^{2} - 24\right) \operatorname{atan}{\left(x \right)}}{x^{2} + 1} - \frac{\left(- 4 x^{2} + 5 x + 3\right)^{2} \left(- \frac{4 x^{2} \operatorname{atan}{\left(x \right)}}{x^{2} + 1} + \frac{3 x}{x^{2} + 1} + \operatorname{atan}{\left(x \right)}\right)}{\left(x^{2} + 1\right)^{2}}\right)
Simplificar
Gráfico
Derivada de y=(4x^2-5x-3)^2*arctg^2x
    © Sr Examen – Калькулятор