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cos(3*x)^(3)*tan(4*x^2+1)^(2)
Derivada de la función/ cos(3*x)^(3)*tan(4*x^2+1)^(2)

Derivada de cos(3*x)^(3)*tan(4*x^2+1)^(2)

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

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Solución

Ha introducido [src] 
   3         2/   2    \
cos (3*x)*tan \4*x  + 1/
cos⁡3(3x)tan⁡2(4x2+1)\cos^{3}{\left(3 x \right)} \tan^{2}{\left(4 x^{2} + 1 \right)} 
cos(3*x)^3*tan(4*x^2 + 1)^2
Gráfica
02468-8-6-4-2-1010-20000002000000
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Trazar el gráfico f'(x)
Primera derivada [src] 
       2         2/   2    \                    3      /       2/   2    \\    /   2    \
- 9*cos (3*x)*tan \4*x  + 1/*sin(3*x) + 16*x*cos (3*x)*\1 + tan \4*x  + 1//*tan\4*x  + 1/
16x(tan⁡2(4x2+1)+1)cos⁡3(3x)tan⁡(4x2+1)−9sin⁡(3x)cos⁡2(3x)tan⁡2(4x2+1)16 x \left(\tan^{2}{\left(4 x^{2} + 1 \right)} + 1\right) \cos^{3}{\left(3 x \right)} \tan{\left(4 x^{2} + 1 \right)} - 9 \sin{\left(3 x \right)} \cos^{2}{\left(3 x \right)} \tan^{2}{\left(4 x^{2} + 1 \right)}
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Segunda derivada [src] 
/      2/       2\ /     2             2     \         2      /       2/       2\\ /   2 /       2/       2\\       2    2/       2\      /       2\\         /       2/       2\\                      /       2\\         
\27*tan \1 + 4*x /*\- cos (3*x) + 2*sin (3*x)/ + 16*cos (3*x)*\1 + tan \1 + 4*x //*\8*x *\1 + tan \1 + 4*x // + 16*x *tan \1 + 4*x / + tan\1 + 4*x // - 288*x*\1 + tan \1 + 4*x //*cos(3*x)*sin(3*x)*tan\1 + 4*x //*cos(3*x)
(−288x(tan⁡2(4x2+1)+1)sin⁡(3x)cos⁡(3x)tan⁡(4x2+1)+27(2sin⁡2(3x)−cos⁡2(3x))tan⁡2(4x2+1)+16(tan⁡2(4x2+1)+1)(8x2(tan⁡2(4x2+1)+1)+16x2tan⁡2(4x2+1)+tan⁡(4x2+1))cos⁡2(3x))cos⁡(3x)\left(- 288 x \left(\tan^{2}{\left(4 x^{2} + 1 \right)} + 1\right) \sin{\left(3 x \right)} \cos{\left(3 x \right)} \tan{\left(4 x^{2} + 1 \right)} + 27 \left(2 \sin^{2}{\left(3 x \right)} - \cos^{2}{\left(3 x \right)}\right) \tan^{2}{\left(4 x^{2} + 1 \right)} + 16 \left(\tan^{2}{\left(4 x^{2} + 1 \right)} + 1\right) \left(8 x^{2} \left(\tan^{2}{\left(4 x^{2} + 1 \right)} + 1\right) + 16 x^{2} \tan^{2}{\left(4 x^{2} + 1 \right)} + \tan{\left(4 x^{2} + 1 \right)}\right) \cos^{2}{\left(3 x \right)}\right) \cos{\left(3 x \right)}
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Tercera derivada [src] 
        2/       2\ /       2             2     \                   2      /       2/       2\\ /   2 /       2/       2\\       2    2/       2\      /       2\\                     3      /       2/       2\\ /         2/       2\       2    3/       2\       2 /       2/       2\\    /       2\\          /       2/       2\\ /     2             2     \             /       2\
- 81*tan \1 + 4*x /*\- 7*cos (3*x) + 2*sin (3*x)/*sin(3*x) - 432*cos (3*x)*\1 + tan \1 + 4*x //*\8*x *\1 + tan \1 + 4*x // + 16*x *tan \1 + 4*x / + tan\1 + 4*x //*sin(3*x) + 128*x*cos (3*x)*\1 + tan \1 + 4*x //*\3 + 9*tan \1 + 4*x / + 32*x *tan \1 + 4*x / + 64*x *\1 + tan \1 + 4*x //*tan\1 + 4*x // + 1296*x*\1 + tan \1 + 4*x //*\- cos (3*x) + 2*sin (3*x)/*cos(3*x)*tan\1 + 4*x /
1296x(2sin⁡2(3x)−cos⁡2(3x))(tan⁡2(4x2+1)+1)cos⁡(3x)tan⁡(4x2+1)+128x(tan⁡2(4x2+1)+1)(64x2(tan⁡2(4x2+1)+1)tan⁡(4x2+1)+32x2tan⁡3(4x2+1)+9tan⁡2(4x2+1)+3)cos⁡3(3x)−81(2sin⁡2(3x)−7cos⁡2(3x))sin⁡(3x)tan⁡2(4x2+1)−432(tan⁡2(4x2+1)+1)(8x2(tan⁡2(4x2+1)+1)+16x2tan⁡2(4x2+1)+tan⁡(4x2+1))sin⁡(3x)cos⁡2(3x)1296 x \left(2 \sin^{2}{\left(3 x \right)} - \cos^{2}{\left(3 x \right)}\right) \left(\tan^{2}{\left(4 x^{2} + 1 \right)} + 1\right) \cos{\left(3 x \right)} \tan{\left(4 x^{2} + 1 \right)} + 128 x \left(\tan^{2}{\left(4 x^{2} + 1 \right)} + 1\right) \left(64 x^{2} \left(\tan^{2}{\left(4 x^{2} + 1 \right)} + 1\right) \tan{\left(4 x^{2} + 1 \right)} + 32 x^{2} \tan^{3}{\left(4 x^{2} + 1 \right)} + 9 \tan^{2}{\left(4 x^{2} + 1 \right)} + 3\right) \cos^{3}{\left(3 x \right)} - 81 \left(2 \sin^{2}{\left(3 x \right)} - 7 \cos^{2}{\left(3 x \right)}\right) \sin{\left(3 x \right)} \tan^{2}{\left(4 x^{2} + 1 \right)} - 432 \left(\tan^{2}{\left(4 x^{2} + 1 \right)} + 1\right) \left(8 x^{2} \left(\tan^{2}{\left(4 x^{2} + 1 \right)} + 1\right) + 16 x^{2} \tan^{2}{\left(4 x^{2} + 1 \right)} + \tan{\left(4 x^{2} + 1 \right)}\right) \sin{\left(3 x \right)} \cos^{2}{\left(3 x \right)}
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Gráfico
Derivada de cos(3*x)^(3)*tan(4*x^2+1)^(2)
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