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y=cos^5(x)^2*tg^3(4x+1)
Derivada de la función/ (x)^2/ y=cos/ y=cos^5(x)^2*tg^3(4x+1)

Derivada de y=cos^5(x)^2*tg^3(4x+1)

Función f() - derivada -er orden en el punto
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Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
   25       3         
cos  (x)*tan (4*x + 1)
cos⁡25(x)tan⁡3(4x+1)\cos^{25}{\left(x \right)} \tan^{3}{\left(4 x + 1 \right)} 
cos(x)^25*tan(4*x + 1)^3
Gráfica
02468-8-6-4-2-1010-500000500000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
   25       2          /           2         \         24       3                
cos  (x)*tan (4*x + 1)*\12 + 12*tan (4*x + 1)/ - 25*cos  (x)*tan (4*x + 1)*sin(x)
(12tan⁡2(4x+1)+12)cos⁡25(x)tan⁡2(4x+1)−25sin⁡(x)cos⁡24(x)tan⁡3(4x+1)\left(12 \tan^{2}{\left(4 x + 1 \right)} + 12\right) \cos^{25}{\left(x \right)} \tan^{2}{\left(4 x + 1 \right)} - 25 \sin{\left(x \right)} \cos^{24}{\left(x \right)} \tan^{3}{\left(4 x + 1 \right)}
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Segunda derivada [src] 
   23    /      2          /     2            2   \         2    /       2         \ /         2         \       /       2         \                           \             
cos  (x)*\25*tan (1 + 4*x)*\- cos (x) + 24*sin (x)/ + 96*cos (x)*\1 + tan (1 + 4*x)/*\1 + 2*tan (1 + 4*x)/ - 600*\1 + tan (1 + 4*x)/*cos(x)*sin(x)*tan(1 + 4*x)/*tan(1 + 4*x)
(25(24sin⁡2(x)−cos⁡2(x))tan⁡2(4x+1)+96(tan⁡2(4x+1)+1)(2tan⁡2(4x+1)+1)cos⁡2(x)−600(tan⁡2(4x+1)+1)sin⁡(x)cos⁡(x)tan⁡(4x+1))cos⁡23(x)tan⁡(4x+1)\left(25 \left(24 \sin^{2}{\left(x \right)} - \cos^{2}{\left(x \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 \right)} - 600 \left(\tan^{2}{\left(4 x + 1 \right)} + 1\right) \sin{\left(x \right)} \cos{\left(x \right)} \tan{\left(4 x + 1 \right)}\right) \cos^{23}{\left(x \right)} \tan{\left(4 x + 1 \right)}
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Tercera derivada [src] 
         /                                                                                         /                   2                                                        \                                                                                                                                                     \
   22    |        3          /        2             2   \                 3    /       2         \ |/       2         \         4                 2          /       2         \|          2          /       2         \ /     2            2   \                  2    /       2         \ /         2         \                    |
cos  (x)*\- 25*tan (1 + 4*x)*\- 73*cos (x) + 552*sin (x)/*sin(x) + 384*cos (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)// + 900*tan (1 + 4*x)*\1 + tan (1 + 4*x)/*\- cos (x) + 24*sin (x)/*cos(x) - 7200*cos (x)*\1 + tan (1 + 4*x)/*\1 + 2*tan (1 + 4*x)/*sin(x)*tan(1 + 4*x)/
(900(24sin⁡2(x)−cos⁡2(x))(tan⁡2(4x+1)+1)cos⁡(x)tan⁡2(4x+1)−25(552sin⁡2(x)−73cos⁡2(x))sin⁡(x)tan⁡3(4x+1)−7200(tan⁡2(4x+1)+1)(2tan⁡2(4x+1)+1)sin⁡(x)cos⁡2(x)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))cos⁡22(x)\left(900 \left(24 \sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) \left(\tan^{2}{\left(4 x + 1 \right)} + 1\right) \cos{\left(x \right)} \tan^{2}{\left(4 x + 1 \right)} - 25 \left(552 \sin^{2}{\left(x \right)} - 73 \cos^{2}{\left(x \right)}\right) \sin{\left(x \right)} \tan^{3}{\left(4 x + 1 \right)} - 7200 \left(\tan^{2}{\left(4 x + 1 \right)} + 1\right) \left(2 \tan^{2}{\left(4 x + 1 \right)} + 1\right) \sin{\left(x \right)} \cos^{2}{\left(x \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 \right)}\right) \cos^{22}{\left(x \right)}
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Gráfico
Derivada de y=cos^5(x)^2*tg^3(4x+1)
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