Sr Examen

Otras calculadoras

y=cos^5x×arccos4x
Derivada de la función/ cos4x/ y=cos/ arccos/ cos^5x/ y=cos^5x×arccos4x

Derivada de y=cos^5x×arccos4x

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
   5             
cos (x)*acos(4*x)
cos⁡5(x)acos⁡(4x)\cos^{5}{\left(x \right)} \operatorname{acos}{\left(4 x \right)} 
cos(x)^5*acos(4*x)
Gráfica
02468-8-6-4-2-10105-5
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
         5                                   
    4*cos (x)           4                    
- -------------- - 5*cos (x)*acos(4*x)*sin(x)
     ___________                             
    /         2                              
  \/  1 - 16*x
−5sin⁡(x)cos⁡4(x)acos⁡(4x)−4cos⁡5(x)1−16x2- 5 \sin{\left(x \right)} \cos^{4}{\left(x \right)} \operatorname{acos}{\left(4 x \right)} - \frac{4 \cos^{5}{\left(x \right)}}{\sqrt{1 - 16 x^{2}}}
Simplificar
Segunda derivada [src] 
        /                                               2                       \
   3    |  /     2           2   \              64*x*cos (x)    40*cos(x)*sin(x)|
cos (x)*|5*\- cos (x) + 4*sin (x)/*acos(4*x) - -------------- + ----------------|
        |                                                 3/2       ___________ |
        |                                      /        2\         /         2  |
        \                                      \1 - 16*x /       \/  1 - 16*x   /
(−64xcos⁡2(x)(1−16x2)32+5(4sin⁡2(x)−cos⁡2(x))acos⁡(4x)+40sin⁡(x)cos⁡(x)1−16x2)cos⁡3(x)\left(- \frac{64 x \cos^{2}{\left(x \right)}}{\left(1 - 16 x^{2}\right)^{\frac{3}{2}}} + 5 \left(4 \sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) \operatorname{acos}{\left(4 x \right)} + \frac{40 \sin{\left(x \right)} \cos{\left(x \right)}}{\sqrt{1 - 16 x^{2}}}\right) \cos^{3}{\left(x \right)}
Simplificar
Tercera derivada [src] 
        /                                                                                                  /           2   \                       \
        |                                                                                             3    |       48*x    |                       |
        |                                                                                       64*cos (x)*|-1 + ----------|                       |
        |     /     2           2   \                                                                      |              2|            2          |
   2    |  60*\- cos (x) + 4*sin (x)/*cos(x)     /        2            2   \                               \     -1 + 16*x /   960*x*cos (x)*sin(x)|
cos (x)*|- --------------------------------- - 5*\- 13*cos (x) + 12*sin (x)/*acos(4*x)*sin(x) + ---------------------------- + --------------------|
        |               ___________                                                                               3/2                        3/2   |
        |              /         2                                                                     /        2\                /        2\      |
        \            \/  1 - 16*x                                                                      \1 - 16*x /                \1 - 16*x /      /
(960xsin⁡(x)cos⁡2(x)(1−16x2)32−5(12sin⁡2(x)−13cos⁡2(x))sin⁡(x)acos⁡(4x)−60(4sin⁡2(x)−cos⁡2(x))cos⁡(x)1−16x2+64(48x216x2−1−1)cos⁡3(x)(1−16x2)32)cos⁡2(x)\left(\frac{960 x \sin{\left(x \right)} \cos^{2}{\left(x \right)}}{\left(1 - 16 x^{2}\right)^{\frac{3}{2}}} - 5 \left(12 \sin^{2}{\left(x \right)} - 13 \cos^{2}{\left(x \right)}\right) \sin{\left(x \right)} \operatorname{acos}{\left(4 x \right)} - \frac{60 \left(4 \sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) \cos{\left(x \right)}}{\sqrt{1 - 16 x^{2}}} + \frac{64 \left(\frac{48 x^{2}}{16 x^{2} - 1} - 1\right) \cos^{3}{\left(x \right)}}{\left(1 - 16 x^{2}\right)^{\frac{3}{2}}}\right) \cos^{2}{\left(x \right)}
Simplificar
Gráfico
Derivada de y=cos^5x×arccos4x
    © Sr Examen – Калькулятор