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

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

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
   5             3         
cos (x + 3)*x*tan (4*x + 1)
xcos⁡5(x+3)tan⁡3(4x+1)x \cos^{5}{\left(x + 3 \right)} \tan^{3}{\left(4 x + 1 \right)} 
(cos(x + 3)^5*x)*tan(4*x + 1)^3
Gráfica
02468-8-6-4-2-1010-1000000000010000000000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
   3          /   5                 4                  \        5           2          /           2         \
tan (4*x + 1)*\cos (x + 3) - 5*x*cos (x + 3)*sin(x + 3)/ + x*cos (x + 3)*tan (4*x + 1)*\12 + 12*tan (4*x + 1)/
x(12tan⁡2(4x+1)+12)cos⁡5(x+3)tan⁡2(4x+1)+(−5xsin⁡(x+3)cos⁡4(x+3)+cos⁡5(x+3))tan⁡3(4x+1)x \left(12 \tan^{2}{\left(4 x + 1 \right)} + 12\right) \cos^{5}{\left(x + 3 \right)} \tan^{2}{\left(4 x + 1 \right)} + \left(- 5 x \sin{\left(x + 3 \right)} \cos^{4}{\left(x + 3 \right)} + \cos^{5}{\left(x + 3 \right)}\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)*\x*\- cos (3 + x) + 4*sin (3 + x)/ - 2*cos(3 + x)*sin(3 + x)/ - 24*\1 + tan (1 + 4*x)/*(-cos(3 + x) + 5*x*sin(3 + x))*cos(3 + x)*tan(1 + 4*x) + 96*x*cos (3 + x)*\1 + tan (1 + 4*x)/*\1 + 2*tan (1 + 4*x)//*tan(1 + 4*x)
(96x(tan⁡2(4x+1)+1)(2tan⁡2(4x+1)+1)cos⁡2(x+3)+5(x(4sin⁡2(x+3)−cos⁡2(x+3))−2sin⁡(x+3)cos⁡(x+3))tan⁡2(4x+1)−24(5xsin⁡(x+3)−cos⁡(x+3))(tan⁡2(4x+1)+1)cos⁡(x+3)tan⁡(4x+1))cos⁡3(x+3)tan⁡(4x+1)\left(96 x \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)} + 5 \left(x \left(4 \sin^{2}{\left(x + 3 \right)} - \cos^{2}{\left(x + 3 \right)}\right) - 2 \sin{\left(x + 3 \right)} \cos{\left(x + 3 \right)}\right) \tan^{2}{\left(4 x + 1 \right)} - 24 \left(5 x \sin{\left(x + 3 \right)} - \cos{\left(x + 3 \right)}\right) \left(\tan^{2}{\left(4 x + 1 \right)} + 1\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)}
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Tercera derivada [src] 
            /                                                                                                                                                                                                                                                                               /                   2                                                        \                                                                                                        \
   2        |       3          /    /     2               2       \                /        2                2       \           \          2          /       2         \ /  /     2               2       \                          \                       3        /       2         \ |/       2         \         4                 2          /       2         \|          2        /       2         \ /         2         \                                            |
cos (3 + x)*\- 5*tan (1 + 4*x)*\- 3*\- cos (3 + x) + 4*sin (3 + x)/*cos(3 + x) + x*\- 13*cos (3 + x) + 12*sin (3 + x)/*sin(3 + x)/ + 180*tan (1 + 4*x)*\1 + tan (1 + 4*x)/*\x*\- cos (3 + x) + 4*sin (3 + x)/ - 2*cos(3 + x)*sin(3 + x)/*cos(3 + x) + 384*x*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)// - 288*cos (3 + x)*\1 + tan (1 + 4*x)/*\1 + 2*tan (1 + 4*x)/*(-cos(3 + x) + 5*x*sin(3 + x))*tan(1 + 4*x)/
(384x(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)+180(x(4sin⁡2(x+3)−cos⁡2(x+3))−2sin⁡(x+3)cos⁡(x+3))(tan⁡2(4x+1)+1)cos⁡(x+3)tan⁡2(4x+1)−288(5xsin⁡(x+3)−cos⁡(x+3))(tan⁡2(4x+1)+1)(2tan⁡2(4x+1)+1)cos⁡2(x+3)tan⁡(4x+1)−5(x(12sin⁡2(x+3)−13cos⁡2(x+3))sin⁡(x+3)−3(4sin⁡2(x+3)−cos⁡2(x+3))cos⁡(x+3))tan⁡3(4x+1))cos⁡2(x+3)\left(384 x \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)} + 180 \left(x \left(4 \sin^{2}{\left(x + 3 \right)} - \cos^{2}{\left(x + 3 \right)}\right) - 2 \sin{\left(x + 3 \right)} \cos{\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)} - 288 \left(5 x \sin{\left(x + 3 \right)} - \cos{\left(x + 3 \right)}\right) \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)} \tan{\left(4 x + 1 \right)} - 5 \left(x \left(12 \sin^{2}{\left(x + 3 \right)} - 13 \cos^{2}{\left(x + 3 \right)}\right) \sin{\left(x + 3 \right)} - 3 \left(4 \sin^{2}{\left(x + 3 \right)} - \cos^{2}{\left(x + 3 \right)}\right) \cos{\left(x + 3 \right)}\right) \tan^{3}{\left(4 x + 1 \right)}\right) \cos^{2}{\left(x + 3 \right)}
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Gráfico
Derivada de y=cos^5(x+3)xtg(4x+1)^3
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