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

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

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

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Solución

Ha introducido [src] 
   5         /         3\
cos (3*x)*tan\(4*x + 1) /
cos⁡5(3x)tan⁡((4x+1)3)\cos^{5}{\left(3 x \right)} \tan{\left(\left(4 x + 1\right)^{3} \right)} 
cos(3*x)^5*tan((4*x + 1)^3)
Gráfica
02468-8-6-4-2-1010-50000005000000
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Trazar el gráfico f'(x)
Primera derivada [src] 
        4                  /         3\               2    5      /       2/         3\\
- 15*cos (3*x)*sin(3*x)*tan\(4*x + 1) / + 12*(4*x + 1) *cos (3*x)*\1 + tan \(4*x + 1) //
12(4x+1)2(tan⁡2((4x+1)3)+1)cos⁡5(3x)−15sin⁡(3x)cos⁡4(3x)tan⁡((4x+1)3)12 \left(4 x + 1\right)^{2} \left(\tan^{2}{\left(\left(4 x + 1\right)^{3} \right)} + 1\right) \cos^{5}{\left(3 x \right)} - 15 \sin{\left(3 x \right)} \cos^{4}{\left(3 x \right)} \tan{\left(\left(4 x + 1\right)^{3} \right)}
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Segunda derivada [src] 
     3      /   /     2             2     \    /         3\                2 /       2/         3\\                           2      /       2/         3\\           /               3    /         3\\\
3*cos (3*x)*\15*\- cos (3*x) + 4*sin (3*x)/*tan\(1 + 4*x) / - 120*(1 + 4*x) *\1 + tan \(1 + 4*x) //*cos(3*x)*sin(3*x) + 32*cos (3*x)*\1 + tan \(1 + 4*x) //*(1 + 4*x)*\1 + 3*(1 + 4*x) *tan\(1 + 4*x) ///
3(−120(4x+1)2(tan⁡2((4x+1)3)+1)sin⁡(3x)cos⁡(3x)+32(4x+1)(3(4x+1)3tan⁡((4x+1)3)+1)(tan⁡2((4x+1)3)+1)cos⁡2(3x)+15(4sin⁡2(3x)−cos⁡2(3x))tan⁡((4x+1)3))cos⁡3(3x)3 \left(- 120 \left(4 x + 1\right)^{2} \left(\tan^{2}{\left(\left(4 x + 1\right)^{3} \right)} + 1\right) \sin{\left(3 x \right)} \cos{\left(3 x \right)} + 32 \left(4 x + 1\right) \left(3 \left(4 x + 1\right)^{3} \tan{\left(\left(4 x + 1\right)^{3} \right)} + 1\right) \left(\tan^{2}{\left(\left(4 x + 1\right)^{3} \right)} + 1\right) \cos^{2}{\left(3 x \right)} + 15 \left(4 \sin^{2}{\left(3 x \right)} - \cos^{2}{\left(3 x \right)}\right) \tan{\left(\left(4 x + 1\right)^{3} \right)}\right) \cos^{3}{\left(3 x \right)}
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Tercera derivada [src] 
            /              /                                               2                                                                                                                          \                                                                                                                                                                                                                                         \
     2      |       3      |       2/         3\     /       2/         3\\           6               3 /       2/         3\\    /         3\               6    2/         3\ /       2/         3\\|      /        2              2     \             /         3\                2 /       2/         3\\ /     2             2     \                    2      /       2/         3\\           /               3    /         3\\         |
3*cos (3*x)*\128*cos (3*x)*\1 + tan \(1 + 4*x) / + 9*\1 + tan \(1 + 4*x) // *(1 + 4*x)  + 18*(1 + 4*x) *\1 + tan \(1 + 4*x) //*tan\(1 + 4*x) / + 18*(1 + 4*x) *tan \(1 + 4*x) /*\1 + tan \(1 + 4*x) /// - 45*\- 13*cos (3*x) + 12*sin (3*x)/*sin(3*x)*tan\(1 + 4*x) / + 540*(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 + 4*x)*\1 + 3*(1 + 4*x) *tan\(1 + 4*x) //*sin(3*x)/
3(540(4x+1)2(4sin⁡2(3x)−cos⁡2(3x))(tan⁡2((4x+1)3)+1)cos⁡(3x)−1440(4x+1)(3(4x+1)3tan⁡((4x+1)3)+1)(tan⁡2((4x+1)3)+1)sin⁡(3x)cos⁡2(3x)−45(12sin⁡2(3x)−13cos⁡2(3x))sin⁡(3x)tan⁡((4x+1)3)+128(9(4x+1)6(tan⁡2((4x+1)3)+1)2+18(4x+1)6(tan⁡2((4x+1)3)+1)tan⁡2((4x+1)3)+18(4x+1)3(tan⁡2((4x+1)3)+1)tan⁡((4x+1)3)+tan⁡2((4x+1)3)+1)cos⁡3(3x))cos⁡2(3x)3 \left(540 \left(4 x + 1\right)^{2} \left(4 \sin^{2}{\left(3 x \right)} - \cos^{2}{\left(3 x \right)}\right) \left(\tan^{2}{\left(\left(4 x + 1\right)^{3} \right)} + 1\right) \cos{\left(3 x \right)} - 1440 \left(4 x + 1\right) \left(3 \left(4 x + 1\right)^{3} \tan{\left(\left(4 x + 1\right)^{3} \right)} + 1\right) \left(\tan^{2}{\left(\left(4 x + 1\right)^{3} \right)} + 1\right) \sin{\left(3 x \right)} \cos^{2}{\left(3 x \right)} - 45 \left(12 \sin^{2}{\left(3 x \right)} - 13 \cos^{2}{\left(3 x \right)}\right) \sin{\left(3 x \right)} \tan{\left(\left(4 x + 1\right)^{3} \right)} + 128 \left(9 \left(4 x + 1\right)^{6} \left(\tan^{2}{\left(\left(4 x + 1\right)^{3} \right)} + 1\right)^{2} + 18 \left(4 x + 1\right)^{6} \left(\tan^{2}{\left(\left(4 x + 1\right)^{3} \right)} + 1\right) \tan^{2}{\left(\left(4 x + 1\right)^{3} \right)} + 18 \left(4 x + 1\right)^{3} \left(\tan^{2}{\left(\left(4 x + 1\right)^{3} \right)} + 1\right) \tan{\left(\left(4 x + 1\right)^{3} \right)} + \tan^{2}{\left(\left(4 x + 1\right)^{3} \right)} + 1\right) \cos^{3}{\left(3 x \right)}\right) \cos^{2}{\left(3 x \right)}
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Gráfico
Derivada de y=cos^5(3x)*tg((4x+1)^3)
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