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

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

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

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Solución

Ha introducido [src]
   2       3         
cos (x)*tan (4*x + 1)
$$\cos^{2}{\left(x \right)} \tan^{3}{\left(4 x + 1 \right)}$$
cos(x)^2*tan(4*x + 1)^3
Gráfica
Primera derivada [src]
   2       2          /           2         \        3                       
cos (x)*tan (4*x + 1)*\12 + 12*tan (4*x + 1)/ - 2*tan (4*x + 1)*cos(x)*sin(x)
$$\left(12 \tan^{2}{\left(4 x + 1 \right)} + 12\right) \cos^{2}{\left(x \right)} \tan^{2}{\left(4 x + 1 \right)} - 2 \sin{\left(x \right)} \cos{\left(x \right)} \tan^{3}{\left(4 x + 1 \right)}$$
Segunda derivada [src]
  /   2          /   2         2   \         2    /       2         \ /         2         \      /       2         \                           \             
2*\tan (1 + 4*x)*\sin (x) - cos (x)/ + 48*cos (x)*\1 + tan (1 + 4*x)/*\1 + 2*tan (1 + 4*x)/ - 24*\1 + tan (1 + 4*x)/*cos(x)*sin(x)*tan(1 + 4*x)/*tan(1 + 4*x)
$$2 \left(\left(\sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) \tan^{2}{\left(4 x + 1 \right)} + 48 \left(\tan^{2}{\left(4 x + 1 \right)} + 1\right) \left(2 \tan^{2}{\left(4 x + 1 \right)} + 1\right) \cos^{2}{\left(x \right)} - 24 \left(\tan^{2}{\left(4 x + 1 \right)} + 1\right) \sin{\left(x \right)} \cos{\left(x \right)} \tan{\left(4 x + 1 \right)}\right) \tan{\left(4 x + 1 \right)}$$
Tercera derivada [src]
  /                                                                                                                       /                   2                                                        \                                                                          \
  |   3                               2          /       2         \ /   2         2   \         2    /       2         \ |/       2         \         4                 2          /       2         \|      /       2         \ /         2         \                           |
8*\tan (1 + 4*x)*cos(x)*sin(x) + 9*tan (1 + 4*x)*\1 + tan (1 + 4*x)/*\sin (x) - cos (x)/ + 48*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)// - 72*\1 + tan (1 + 4*x)/*\1 + 2*tan (1 + 4*x)/*cos(x)*sin(x)*tan(1 + 4*x)/
$$8 \left(9 \left(\sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) \left(\tan^{2}{\left(4 x + 1 \right)} + 1\right) \tan^{2}{\left(4 x + 1 \right)} - 72 \left(\tan^{2}{\left(4 x + 1 \right)} + 1\right) \left(2 \tan^{2}{\left(4 x + 1 \right)} + 1\right) \sin{\left(x \right)} \cos{\left(x \right)} \tan{\left(4 x + 1 \right)} + 48 \left(\tan^{2}{\left(4 x + 1 \right)} + 1\right) \left(\left(\tan^{2}{\left(4 x + 1 \right)} + 1\right)^{2} + 7 \left(\tan^{2}{\left(4 x + 1 \right)} + 1\right) \tan^{2}{\left(4 x + 1 \right)} + 2 \tan^{4}{\left(4 x + 1 \right)}\right) \cos^{2}{\left(x \right)} + \sin{\left(x \right)} \cos{\left(x \right)} \tan^{3}{\left(4 x + 1 \right)}\right)$$
Gráfico
Derivada de y=cos(x)^2*tg^3(4x+1)