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y=cos^5(x+3)*tg(4x+1)^3
Derivada de la función/ y=cos/ (x+3)/ y=cos^5(x+3)*tg(4x+1)^3

Derivada de y=cos^5(x+3)*tg(4x+1)^3

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
   5           3         
cos (x + 3)*tan (4*x + 1)
cos⁡5(x+3)tan⁡3(4x+1)\cos^{5}{\left(x + 3 \right)} \tan^{3}{\left(4 x + 1 \right)} 
cos(x + 3)^5*tan(4*x + 1)^3
Gráfica
02468-8-6-4-2-1010-20000000002000000000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
   5           2          /           2         \        4           3                    
cos (x + 3)*tan (4*x + 1)*\12 + 12*tan (4*x + 1)/ - 5*cos (x + 3)*tan (4*x + 1)*sin(x + 3)
(12tan⁡2(4x+1)+12)cos⁡5(x+3)tan⁡2(4x+1)−5sin⁡(x+3)cos⁡4(x+3)tan⁡3(4x+1)\left(12 \tan^{2}{\left(4 x + 1 \right)} + 12\right) \cos^{5}{\left(x + 3 \right)} \tan^{2}{\left(4 x + 1 \right)} - 5 \sin{\left(x + 3 \right)} \cos^{4}{\left(x + 3 \right)} \tan^{3}{\left(4 x + 1 \right)}
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Segunda derivada [src] 
   3        /     2          /     2               2       \         2        /       2         \ /         2         \       /       2         \                                   \             
cos (3 + x)*\5*tan (1 + 4*x)*\- cos (3 + x) + 4*sin (3 + x)/ + 96*cos (3 + x)*\1 + tan (1 + 4*x)/*\1 + 2*tan (1 + 4*x)/ - 120*\1 + tan (1 + 4*x)/*cos(3 + x)*sin(3 + x)*tan(1 + 4*x)/*tan(1 + 4*x)
(5(4sin⁡2(x+3)−cos⁡2(x+3))tan⁡2(4x+1)+96(tan⁡2(4x+1)+1)(2tan⁡2(4x+1)+1)cos⁡2(x+3)−120(tan⁡2(4x+1)+1)sin⁡(x+3)cos⁡(x+3)tan⁡(4x+1))cos⁡3(x+3)tan⁡(4x+1)\left(5 \left(4 \sin^{2}{\left(x + 3 \right)} - \cos^{2}{\left(x + 3 \right)}\right) \tan^{2}{\left(4 x + 1 \right)} + 96 \left(\tan^{2}{\left(4 x + 1 \right)} + 1\right) \left(2 \tan^{2}{\left(4 x + 1 \right)} + 1\right) \cos^{2}{\left(x + 3 \right)} - 120 \left(\tan^{2}{\left(4 x + 1 \right)} + 1\right) \sin{\left(x + 3 \right)} \cos{\left(x + 3 \right)} \tan{\left(4 x + 1 \right)}\right) \cos^{3}{\left(x + 3 \right)} \tan{\left(4 x + 1 \right)}
Simplificar
Tercera derivada [src] 
            /                                                                                                       /                   2                                                        \                                                                                                                                                                        \
   2        |       3          /        2                2       \                     3        /       2         \ |/       2         \         4                 2          /       2         \|          2          /       2         \ /     2               2       \                      2        /       2         \ /         2         \                        |
cos (3 + x)*\- 5*tan (1 + 4*x)*\- 13*cos (3 + x) + 12*sin (3 + x)/*sin(3 + x) + 384*cos (3 + x)*\1 + tan (1 + 4*x)/*\\1 + tan (1 + 4*x)/  + 2*tan (1 + 4*x) + 7*tan (1 + 4*x)*\1 + tan (1 + 4*x)// + 180*tan (1 + 4*x)*\1 + tan (1 + 4*x)/*\- cos (3 + x) + 4*sin (3 + x)/*cos(3 + x) - 1440*cos (3 + x)*\1 + tan (1 + 4*x)/*\1 + 2*tan (1 + 4*x)/*sin(3 + x)*tan(1 + 4*x)/
(180(4sin⁡2(x+3)−cos⁡2(x+3))(tan⁡2(4x+1)+1)cos⁡(x+3)tan⁡2(4x+1)−5(12sin⁡2(x+3)−13cos⁡2(x+3))sin⁡(x+3)tan⁡3(4x+1)−1440(tan⁡2(4x+1)+1)(2tan⁡2(4x+1)+1)sin⁡(x+3)cos⁡2(x+3)tan⁡(4x+1)+384(tan⁡2(4x+1)+1)((tan⁡2(4x+1)+1)2+7(tan⁡2(4x+1)+1)tan⁡2(4x+1)+2tan⁡4(4x+1))cos⁡3(x+3))cos⁡2(x+3)\left(180 \left(4 \sin^{2}{\left(x + 3 \right)} - \cos^{2}{\left(x + 3 \right)}\right) \left(\tan^{2}{\left(4 x + 1 \right)} + 1\right) \cos{\left(x + 3 \right)} \tan^{2}{\left(4 x + 1 \right)} - 5 \left(12 \sin^{2}{\left(x + 3 \right)} - 13 \cos^{2}{\left(x + 3 \right)}\right) \sin{\left(x + 3 \right)} \tan^{3}{\left(4 x + 1 \right)} - 1440 \left(\tan^{2}{\left(4 x + 1 \right)} + 1\right) \left(2 \tan^{2}{\left(4 x + 1 \right)} + 1\right) \sin{\left(x + 3 \right)} \cos^{2}{\left(x + 3 \right)} \tan{\left(4 x + 1 \right)} + 384 \left(\tan^{2}{\left(4 x + 1 \right)} + 1\right) \left(\left(\tan^{2}{\left(4 x + 1 \right)} + 1\right)^{2} + 7 \left(\tan^{2}{\left(4 x + 1 \right)} + 1\right) \tan^{2}{\left(4 x + 1 \right)} + 2 \tan^{4}{\left(4 x + 1 \right)}\right) \cos^{3}{\left(x + 3 \right)}\right) \cos^{2}{\left(x + 3 \right)}
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Gráfico
Derivada de y=cos^5(x+3)*tg(4x+1)^3
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