Sr Examen

Otras calculadoras

y=sin^4*3x*arctg2x^3
Derivada de la función/ arctg/ ctg2x/ sin^4/ y=sin/ y=sin^4*3x*arctg2x^3

Derivada de y=sin^4*3x*arctg2x^3

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
   4          3     
sin (3)*x*atan (2*x)
xsin⁡4(3)atan⁡3(2x)x \sin^{4}{\left(3 \right)} \operatorname{atan}^{3}{\left(2 x \right)} 
(sin(3)^4*x)*atan(2*x)^3
Gráfica
02468-8-6-4-2-10100.02-0.02
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
                             2         4   
    3         4      6*x*atan (2*x)*sin (3)
atan (2*x)*sin (3) + ----------------------
                                   2       
                            1 + 4*x
6xsin⁡4(3)atan⁡2(2x)4x2+1+sin⁡4(3)atan⁡3(2x)\frac{6 x \sin^{4}{\left(3 \right)} \operatorname{atan}^{2}{\left(2 x \right)}}{4 x^{2} + 1} + \sin^{4}{\left(3 \right)} \operatorname{atan}^{3}{\left(2 x \right)}
Simplificar
Segunda derivada [src] 
      4    /  2*x*(-1 + 2*x*atan(2*x))            \          
12*sin (3)*|- ------------------------ + atan(2*x)|*atan(2*x)
           |                 2                    |          
           \          1 + 4*x                     /          
-------------------------------------------------------------
                                  2                          
                           1 + 4*x
12(−2x(2xatan⁡(2x)−1)4x2+1+atan⁡(2x))sin⁡4(3)atan⁡(2x)4x2+1\frac{12 \left(- \frac{2 x \left(2 x \operatorname{atan}{\left(2 x \right)} - 1\right)}{4 x^{2} + 1} + \operatorname{atan}{\left(2 x \right)}\right) \sin^{4}{\left(3 \right)} \operatorname{atan}{\left(2 x \right)}}{4 x^{2} + 1}
Simplificar
Tercera derivada [src] 
           /                                        /                                             2     2     \\
      4    |                                        |   1           2        12*x*atan(2*x)   16*x *atan (2*x)||
24*sin (3)*|-3*(-1 + 2*x*atan(2*x))*atan(2*x) + 2*x*|-------- - atan (2*x) - -------------- + ----------------||
           |                                        |       2                          2                 2    ||
           \                                        \1 + 4*x                    1 + 4*x           1 + 4*x     //
----------------------------------------------------------------------------------------------------------------
                                                            2                                                   
                                                  /       2\                                                    
                                                  \1 + 4*x /
24(2x(16x2atan⁡2(2x)4x2+1−12xatan⁡(2x)4x2+1−atan⁡2(2x)+14x2+1)−3(2xatan⁡(2x)−1)atan⁡(2x))sin⁡4(3)(4x2+1)2\frac{24 \left(2 x \left(\frac{16 x^{2} \operatorname{atan}^{2}{\left(2 x \right)}}{4 x^{2} + 1} - \frac{12 x \operatorname{atan}{\left(2 x \right)}}{4 x^{2} + 1} - \operatorname{atan}^{2}{\left(2 x \right)} + \frac{1}{4 x^{2} + 1}\right) - 3 \left(2 x \operatorname{atan}{\left(2 x \right)} - 1\right) \operatorname{atan}{\left(2 x \right)}\right) \sin^{4}{\left(3 \right)}}{\left(4 x^{2} + 1\right)^{2}}
Simplificar
Gráfico
Derivada de y=sin^4*3x*arctg2x^3
    © Sr Examen – Калькулятор