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tan(2x^2-1)/sin(2x^2-1)
Derivada de la función/ x^2-1/ tan(2x^2-1)/sin(2x^2-1)

Derivada de tan(2x^2-1)/sin(2x^2-1)

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
   /   2    \
tan\2*x  - 1/
-------------
   /   2    \
sin\2*x  - 1/
tan⁡(2x2−1)sin⁡(2x2−1)\frac{\tan{\left(2 x^{2} - 1 \right)}}{\sin{\left(2 x^{2} - 1 \right)}} 
tan(2*x^2 - 1)/sin(2*x^2 - 1)
Gráfica
02468-8-6-4-2-1010-1000010000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
    /       2/   2    \\          /   2    \    /   2    \
4*x*\1 + tan \2*x  - 1//   4*x*cos\2*x  - 1/*tan\2*x  - 1/
------------------------ - -------------------------------
        /   2    \                     2/   2    \        
     sin\2*x  - 1/                  sin \2*x  - 1/
4x(tan⁡2(2x2−1)+1)sin⁡(2x2−1)−4xcos⁡(2x2−1)tan⁡(2x2−1)sin⁡2(2x2−1)\frac{4 x \left(\tan^{2}{\left(2 x^{2} - 1 \right)} + 1\right)}{\sin{\left(2 x^{2} - 1 \right)}} - \frac{4 x \cos{\left(2 x^{2} - 1 \right)} \tan{\left(2 x^{2} - 1 \right)}}{\sin^{2}{\left(2 x^{2} - 1 \right)}}
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Segunda derivada [src] 
  /                      /          /        2\      2    2/        2\\                                                                 2 /       2/        2\\    /        2\\
  |       2/        2\   |   2   cos\-1 + 2*x /   8*x *cos \-1 + 2*x /|    /        2\      2 /       2/        2\\    /        2\   8*x *\1 + tan \-1 + 2*x //*cos\-1 + 2*x /|
4*|1 + tan \-1 + 2*x / + |4*x  - -------------- + --------------------|*tan\-1 + 2*x / + 8*x *\1 + tan \-1 + 2*x //*tan\-1 + 2*x / - -----------------------------------------|
  |                      |          /        2\        2/        2\   |                                                                               /        2\             |
  \                      \       sin\-1 + 2*x /     sin \-1 + 2*x /   /                                                                            sin\-1 + 2*x /             /
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                                                                                    /        2\                                                                                
                                                                                 sin\-1 + 2*x /
4(8x2(tan⁡2(2x2−1)+1)tan⁡(2x2−1)−8x2(tan⁡2(2x2−1)+1)cos⁡(2x2−1)sin⁡(2x2−1)+(4x2+8x2cos⁡2(2x2−1)sin⁡2(2x2−1)−cos⁡(2x2−1)sin⁡(2x2−1))tan⁡(2x2−1)+tan⁡2(2x2−1)+1)sin⁡(2x2−1)\frac{4 \left(8 x^{2} \left(\tan^{2}{\left(2 x^{2} - 1 \right)} + 1\right) \tan{\left(2 x^{2} - 1 \right)} - \frac{8 x^{2} \left(\tan^{2}{\left(2 x^{2} - 1 \right)} + 1\right) \cos{\left(2 x^{2} - 1 \right)}}{\sin{\left(2 x^{2} - 1 \right)}} + \left(4 x^{2} + \frac{8 x^{2} \cos^{2}{\left(2 x^{2} - 1 \right)}}{\sin^{2}{\left(2 x^{2} - 1 \right)}} - \frac{\cos{\left(2 x^{2} - 1 \right)}}{\sin{\left(2 x^{2} - 1 \right)}}\right) \tan{\left(2 x^{2} - 1 \right)} + \tan^{2}{\left(2 x^{2} - 1 \right)} + 1\right)}{\sin{\left(2 x^{2} - 1 \right)}}
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Tercera derivada [src] 
     /  /          2/        2\       2    /        2\       2    3/        2\\                                                                                                                                           /          /        2\      2    2/        2\\     /       2/        2\      2 /       2/        2\\    /        2\\    /        2\\
     |  |     6*cos \-1 + 2*x /   20*x *cos\-1 + 2*x /   24*x *cos \-1 + 2*x /|    /        2\     /       2/        2\\ /     /        2\      2 /       2/        2\\      2    2/        2\\     /       2/        2\\ |   2   cos\-1 + 2*x /   8*x *cos \-1 + 2*x /|   3*\1 + tan \-1 + 2*x / + 8*x *\1 + tan \-1 + 2*x //*tan\-1 + 2*x //*cos\-1 + 2*x /|
16*x*|- |-3 - ----------------- + -------------------- + ---------------------|*tan\-1 + 2*x / + 2*\1 + tan \-1 + 2*x //*\3*tan\-1 + 2*x / + 4*x *\1 + tan \-1 + 2*x // + 8*x *tan \-1 + 2*x // + 3*\1 + tan \-1 + 2*x //*|4*x  - -------------- + --------------------| - ----------------------------------------------------------------------------------|
     |  |         2/        2\          /        2\            3/        2\   |                                                                                                                                           |          /        2\        2/        2\   |                                        /        2\                                  |
     \  \      sin \-1 + 2*x /       sin\-1 + 2*x /         sin \-1 + 2*x /   /                                                                                                                                           \       sin\-1 + 2*x /     sin \-1 + 2*x /   /                                     sin\-1 + 2*x /                                  /
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                                                                                                                                                                           /        2\                                                                                                                                                                        
                                                                                                                                                                        sin\-1 + 2*x /
16x(3(tan⁡2(2x2−1)+1)(4x2+8x2cos⁡2(2x2−1)sin⁡2(2x2−1)−cos⁡(2x2−1)sin⁡(2x2−1))+2(tan⁡2(2x2−1)+1)(4x2(tan⁡2(2x2−1)+1)+8x2tan⁡2(2x2−1)+3tan⁡(2x2−1))−3(8x2(tan⁡2(2x2−1)+1)tan⁡(2x2−1)+tan⁡2(2x2−1)+1)cos⁡(2x2−1)sin⁡(2x2−1)−(20x2cos⁡(2x2−1)sin⁡(2x2−1)+24x2cos⁡3(2x2−1)sin⁡3(2x2−1)−3−6cos⁡2(2x2−1)sin⁡2(2x2−1))tan⁡(2x2−1))sin⁡(2x2−1)\frac{16 x \left(3 \left(\tan^{2}{\left(2 x^{2} - 1 \right)} + 1\right) \left(4 x^{2} + \frac{8 x^{2} \cos^{2}{\left(2 x^{2} - 1 \right)}}{\sin^{2}{\left(2 x^{2} - 1 \right)}} - \frac{\cos{\left(2 x^{2} - 1 \right)}}{\sin{\left(2 x^{2} - 1 \right)}}\right) + 2 \left(\tan^{2}{\left(2 x^{2} - 1 \right)} + 1\right) \left(4 x^{2} \left(\tan^{2}{\left(2 x^{2} - 1 \right)} + 1\right) + 8 x^{2} \tan^{2}{\left(2 x^{2} - 1 \right)} + 3 \tan{\left(2 x^{2} - 1 \right)}\right) - \frac{3 \left(8 x^{2} \left(\tan^{2}{\left(2 x^{2} - 1 \right)} + 1\right) \tan{\left(2 x^{2} - 1 \right)} + \tan^{2}{\left(2 x^{2} - 1 \right)} + 1\right) \cos{\left(2 x^{2} - 1 \right)}}{\sin{\left(2 x^{2} - 1 \right)}} - \left(\frac{20 x^{2} \cos{\left(2 x^{2} - 1 \right)}}{\sin{\left(2 x^{2} - 1 \right)}} + \frac{24 x^{2} \cos^{3}{\left(2 x^{2} - 1 \right)}}{\sin^{3}{\left(2 x^{2} - 1 \right)}} - 3 - \frac{6 \cos^{2}{\left(2 x^{2} - 1 \right)}}{\sin^{2}{\left(2 x^{2} - 1 \right)}}\right) \tan{\left(2 x^{2} - 1 \right)}\right)}{\sin{\left(2 x^{2} - 1 \right)}}
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Gráfico
Derivada de tan(2x^2-1)/sin(2x^2-1)
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