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y=cos^2(cbrt(tg2^arcsinx))+exp^tg(x^2)
Derivada de la función/ y=cos^2(cbrt(tg2^arcsinx))+exp^tg(x^2)

Derivada de y=cos^2(cbrt(tg2^arcsinx))+exp^tg(x^2)

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
    /   _______________\       / 2\
   2|3 /    asin(x)    |    tan\x /
cos \\/  tan       (2) / + E
etan⁡(x2)+cos⁡2(tan⁡asin⁡(x)(2)3)e^{\tan{\left(x^{2} \right)}} + \cos^{2}{\left(\sqrt[3]{\tan^{\operatorname{asin}{\left(x \right)}}{\left(2 \right)}} \right)} 
cos((tan(2)^asin(x))^(1/3))^2 + E^tan(x^2)
Gráfica
02468-8-6-4-2-1010-2500000025000000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
                                   _______________                          /   _______________\    /   _______________\
                       / 2\     3 /    asin(x)                              |3 /    asin(x)    |    |3 /    asin(x)    |
    /       2/ 2\\  tan\x /   2*\/  tan       (2) *(pi*I + log(-tan(2)))*cos\\/  tan       (2) /*sin\\/  tan       (2) /
2*x*\1 + tan \x //*e        - ------------------------------------------------------------------------------------------
                                                                         ________                                       
                                                                        /      2                                        
                                                                    3*\/  1 - x
2x(tan⁡2(x2)+1)etan⁡(x2)−2(log⁡(−tan⁡(2))+iπ)tan⁡asin⁡(x)(2)3sin⁡(tan⁡asin⁡(x)(2)3)cos⁡(tan⁡asin⁡(x)(2)3)31−x22 x \left(\tan^{2}{\left(x^{2} \right)} + 1\right) e^{\tan{\left(x^{2} \right)}} - \frac{2 \left(\log{\left(- \tan{\left(2 \right)} \right)} + i \pi\right) \sqrt[3]{\tan^{\operatorname{asin}{\left(x \right)}}{\left(2 \right)}} \sin{\left(\sqrt[3]{\tan^{\operatorname{asin}{\left(x \right)}}{\left(2 \right)}} \right)} \cos{\left(\sqrt[3]{\tan^{\operatorname{asin}{\left(x \right)}}{\left(2 \right)}} \right)}}{3 \sqrt{1 - x^{2}}}
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Segunda derivada [src] 
  /                                                                                                              2/3                            /   _______________\                2/3                            /   _______________\      _______________                           /   _______________\    /   _______________\        _______________                          /   _______________\    /   _______________\\
  |                   / 2\                      2     / 2\                           / 2\              asin(x)                            2    2|3 /    asin(x)    |      asin(x)                            2    2|3 /    asin(x)    |   3 /    asin(x)                          2    |3 /    asin(x)    |    |3 /    asin(x)    |     3 /    asin(x)                              |3 /    asin(x)    |    |3 /    asin(x)    ||
  |/       2/ 2\\  tan\x /      2 /       2/ 2\\   tan\x /      2 /       2/ 2\\  tan\x /    / 2\   tan       (2)   *(pi*I + log(-tan(2))) *sin \\/  tan       (2) /   tan       (2)   *(pi*I + log(-tan(2))) *cos \\/  tan       (2) /   \/  tan       (2) *(pi*I + log(-tan(2))) *cos\\/  tan       (2) /*sin\\/  tan       (2) /   x*\/  tan       (2) *(pi*I + log(-tan(2)))*cos\\/  tan       (2) /*sin\\/  tan       (2) /|
2*|\1 + tan \x //*e        + 2*x *\1 + tan \x // *e        + 4*x *\1 + tan \x //*e       *tan\x / - ---------------------------------------------------------------- + ---------------------------------------------------------------- + ----------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------|
  |                                                                                                                             /      2\                                                          /      2\                                                                       /      2\                                                                                          3/2                                       |
  |                                                                                                                           9*\-1 + x /                                                        9*\-1 + x /                                                                     9*\-1 + x /                                                                                  /     2\                                          |
  \                                                                                                                                                                                                                                                                                                                                                                         3*\1 - x /                                          /
2(2x2(tan⁡2(x2)+1)2etan⁡(x2)+4x2(tan⁡2(x2)+1)etan⁡(x2)tan⁡(x2)−x(log⁡(−tan⁡(2))+iπ)tan⁡asin⁡(x)(2)3sin⁡(tan⁡asin⁡(x)(2)3)cos⁡(tan⁡asin⁡(x)(2)3)3(1−x2)32+(tan⁡2(x2)+1)etan⁡(x2)−(log⁡(−tan⁡(2))+iπ)2(tan⁡asin⁡(x)(2))23sin⁡2(tan⁡asin⁡(x)(2)3)9(x2−1)+(log⁡(−tan⁡(2))+iπ)2(tan⁡asin⁡(x)(2))23cos⁡2(tan⁡asin⁡(x)(2)3)9(x2−1)+(log⁡(−tan⁡(2))+iπ)2tan⁡asin⁡(x)(2)3sin⁡(tan⁡asin⁡(x)(2)3)cos⁡(tan⁡asin⁡(x)(2)3)9(x2−1))2 \left(2 x^{2} \left(\tan^{2}{\left(x^{2} \right)} + 1\right)^{2} e^{\tan{\left(x^{2} \right)}} + 4 x^{2} \left(\tan^{2}{\left(x^{2} \right)} + 1\right) e^{\tan{\left(x^{2} \right)}} \tan{\left(x^{2} \right)} - \frac{x \left(\log{\left(- \tan{\left(2 \right)} \right)} + i \pi\right) \sqrt[3]{\tan^{\operatorname{asin}{\left(x \right)}}{\left(2 \right)}} \sin{\left(\sqrt[3]{\tan^{\operatorname{asin}{\left(x \right)}}{\left(2 \right)}} \right)} \cos{\left(\sqrt[3]{\tan^{\operatorname{asin}{\left(x \right)}}{\left(2 \right)}} \right)}}{3 \left(1 - x^{2}\right)^{\frac{3}{2}}} + \left(\tan^{2}{\left(x^{2} \right)} + 1\right) e^{\tan{\left(x^{2} \right)}} - \frac{\left(\log{\left(- \tan{\left(2 \right)} \right)} + i \pi\right)^{2} \left(\tan^{\operatorname{asin}{\left(x \right)}}{\left(2 \right)}\right)^{\frac{2}{3}} \sin^{2}{\left(\sqrt[3]{\tan^{\operatorname{asin}{\left(x \right)}}{\left(2 \right)}} \right)}}{9 \left(x^{2} - 1\right)} + \frac{\left(\log{\left(- \tan{\left(2 \right)} \right)} + i \pi\right)^{2} \left(\tan^{\operatorname{asin}{\left(x \right)}}{\left(2 \right)}\right)^{\frac{2}{3}} \cos^{2}{\left(\sqrt[3]{\tan^{\operatorname{asin}{\left(x \right)}}{\left(2 \right)}} \right)}}{9 \left(x^{2} - 1\right)} + \frac{\left(\log{\left(- \tan{\left(2 \right)} \right)} + i \pi\right)^{2} \sqrt[3]{\tan^{\operatorname{asin}{\left(x \right)}}{\left(2 \right)}} \sin{\left(\sqrt[3]{\tan^{\operatorname{asin}{\left(x \right)}}{\left(2 \right)}} \right)} \cos{\left(\sqrt[3]{\tan^{\operatorname{asin}{\left(x \right)}}{\left(2 \right)}} \right)}}{9 \left(x^{2} - 1\right)}\right)
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Tercera derivada [src] 
  /                                                                                                                                                                                                                                     2/3                            /   _______________\                2/3                            /   _______________\                  2/3                            /   _______________\      _______________                          /   _______________\    /   _______________\      _______________                           /   _______________\    /   _______________\                  2/3                            /   _______________\                                             /   _______________\    /   _______________\         _______________                          /   _______________\    /   _______________\        _______________                           /   _______________\    /   _______________\\
  |                   3     / 2\                     2     / 2\                      2     / 2\                           / 2\                                             / 2\                       2     / 2\              asin(x)                            3    2|3 /    asin(x)    |      asin(x)                            3    2|3 /    asin(x)    |        asin(x)                            2    2|3 /    asin(x)    |   3 /    asin(x)                              |3 /    asin(x)    |    |3 /    asin(x)    |   3 /    asin(x)                          3    |3 /    asin(x)    |    |3 /    asin(x)    |        asin(x)                            2    2|3 /    asin(x)    |                          3    asin(x)       |3 /    asin(x)    |    |3 /    asin(x)    |    2 3 /    asin(x)                              |3 /    asin(x)    |    |3 /    asin(x)    |     3 /    asin(x)                          2    |3 /    asin(x)    |    |3 /    asin(x)    ||
  |   3 /       2/ 2\\   tan\x /       /       2/ 2\\   tan\x /      3 /       2/ 2\\   tan\x /        /       2/ 2\\  tan\x /    / 2\       3    2/ 2\ /       2/ 2\\  tan\x /       3 /       2/ 2\\   tan\x /    / 2\   tan       (2)   *(pi*I + log(-tan(2))) *cos \\/  tan       (2) /   tan       (2)   *(pi*I + log(-tan(2))) *sin \\/  tan       (2) /   x*tan       (2)   *(pi*I + log(-tan(2))) *cos \\/  tan       (2) /   \/  tan       (2) *(pi*I + log(-tan(2)))*cos\\/  tan       (2) /*sin\\/  tan       (2) /   \/  tan       (2) *(pi*I + log(-tan(2))) *cos\\/  tan       (2) /*sin\\/  tan       (2) /   x*tan       (2)   *(pi*I + log(-tan(2))) *sin \\/  tan       (2) /   4*(pi*I + log(-tan(2))) *tan       (2)*cos\\/  tan       (2) /*sin\\/  tan       (2) /   x *\/  tan       (2) *(pi*I + log(-tan(2)))*cos\\/  tan       (2) /*sin\\/  tan       (2) /   x*\/  tan       (2) *(pi*I + log(-tan(2))) *cos\\/  tan       (2) /*sin\\/  tan       (2) /|
2*|4*x *\1 + tan \x // *e        + 6*x*\1 + tan \x // *e        + 8*x *\1 + tan \x // *e        + 12*x*\1 + tan \x //*e       *tan\x / + 16*x *tan \x /*\1 + tan \x //*e        + 24*x *\1 + tan \x // *e       *tan\x / - ---------------------------------------------------------------- + ---------------------------------------------------------------- - ------------------------------------------------------------------ - ---------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------- + ------------------------------------------------------------------ + -------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------|
  |                                                                                                                                                                                                                                                           3/2                                                                3/2                                                                   2                                                                             3/2                                                                                          3/2                                                                              2                                                                             3/2                                                                                       5/2                                                                                              2                                       |
  |                                                                                                                                                                                                                                                   /     2\                                                           /     2\                                                             /      2\                                                                      /     2\                                                                                     /     2\                                                                        /      2\                                                                      /     2\                                                                                  /     2\                                                                                        /      2\                                        |
  \                                                                                                                                                                                                                                                 9*\1 - x /                                                         9*\1 - x /                                                           3*\-1 + x /                                                                    3*\1 - x /                                                                                  27*\1 - x /                                                                      3*\-1 + x /                                                                   27*\1 - x /                                                                                  \1 - x /                                                                                      3*\-1 + x /                                        /
2(4x3(tan⁡2(x2)+1)3etan⁡(x2)+24x3(tan⁡2(x2)+1)2etan⁡(x2)tan⁡(x2)+8x3(tan⁡2(x2)+1)2etan⁡(x2)+16x3(tan⁡2(x2)+1)etan⁡(x2)tan⁡2(x2)−x2(log⁡(−tan⁡(2))+iπ)tan⁡asin⁡(x)(2)3sin⁡(tan⁡asin⁡(x)(2)3)cos⁡(tan⁡asin⁡(x)(2)3)(1−x2)52+6x(tan⁡2(x2)+1)2etan⁡(x2)+12x(tan⁡2(x2)+1)etan⁡(x2)tan⁡(x2)+x(log⁡(−tan⁡(2))+iπ)2(tan⁡asin⁡(x)(2))23sin⁡2(tan⁡asin⁡(x)(2)3)3(x2−1)2−x(log⁡(−tan⁡(2))+iπ)2(tan⁡asin⁡(x)(2))23cos⁡2(tan⁡asin⁡(x)(2)3)3(x2−1)2−x(log⁡(−tan⁡(2))+iπ)2tan⁡asin⁡(x)(2)3sin⁡(tan⁡asin⁡(x)(2)3)cos⁡(tan⁡asin⁡(x)(2)3)3(x2−1)2+(log⁡(−tan⁡(2))+iπ)3(tan⁡asin⁡(x)(2))23sin⁡2(tan⁡asin⁡(x)(2)3)9(1−x2)32−(log⁡(−tan⁡(2))+iπ)3(tan⁡asin⁡(x)(2))23cos⁡2(tan⁡asin⁡(x)(2)3)9(1−x2)32−(log⁡(−tan⁡(2))+iπ)tan⁡asin⁡(x)(2)3sin⁡(tan⁡asin⁡(x)(2)3)cos⁡(tan⁡asin⁡(x)(2)3)3(1−x2)32−(log⁡(−tan⁡(2))+iπ)3tan⁡asin⁡(x)(2)3sin⁡(tan⁡asin⁡(x)(2)3)cos⁡(tan⁡asin⁡(x)(2)3)27(1−x2)32+4(log⁡(−tan⁡(2))+iπ)3sin⁡(tan⁡asin⁡(x)(2)3)cos⁡(tan⁡asin⁡(x)(2)3)tan⁡asin⁡(x)(2)27(1−x2)32)2 \left(4 x^{3} \left(\tan^{2}{\left(x^{2} \right)} + 1\right)^{3} e^{\tan{\left(x^{2} \right)}} + 24 x^{3} \left(\tan^{2}{\left(x^{2} \right)} + 1\right)^{2} e^{\tan{\left(x^{2} \right)}} \tan{\left(x^{2} \right)} + 8 x^{3} \left(\tan^{2}{\left(x^{2} \right)} + 1\right)^{2} e^{\tan{\left(x^{2} \right)}} + 16 x^{3} \left(\tan^{2}{\left(x^{2} \right)} + 1\right) e^{\tan{\left(x^{2} \right)}} \tan^{2}{\left(x^{2} \right)} - \frac{x^{2} \left(\log{\left(- \tan{\left(2 \right)} \right)} + i \pi\right) \sqrt[3]{\tan^{\operatorname{asin}{\left(x \right)}}{\left(2 \right)}} \sin{\left(\sqrt[3]{\tan^{\operatorname{asin}{\left(x \right)}}{\left(2 \right)}} \right)} \cos{\left(\sqrt[3]{\tan^{\operatorname{asin}{\left(x \right)}}{\left(2 \right)}} \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + 6 x \left(\tan^{2}{\left(x^{2} \right)} + 1\right)^{2} e^{\tan{\left(x^{2} \right)}} + 12 x \left(\tan^{2}{\left(x^{2} \right)} + 1\right) e^{\tan{\left(x^{2} \right)}} \tan{\left(x^{2} \right)} + \frac{x \left(\log{\left(- \tan{\left(2 \right)} \right)} + i \pi\right)^{2} \left(\tan^{\operatorname{asin}{\left(x \right)}}{\left(2 \right)}\right)^{\frac{2}{3}} \sin^{2}{\left(\sqrt[3]{\tan^{\operatorname{asin}{\left(x \right)}}{\left(2 \right)}} \right)}}{3 \left(x^{2} - 1\right)^{2}} - \frac{x \left(\log{\left(- \tan{\left(2 \right)} \right)} + i \pi\right)^{2} \left(\tan^{\operatorname{asin}{\left(x \right)}}{\left(2 \right)}\right)^{\frac{2}{3}} \cos^{2}{\left(\sqrt[3]{\tan^{\operatorname{asin}{\left(x \right)}}{\left(2 \right)}} \right)}}{3 \left(x^{2} - 1\right)^{2}} - \frac{x \left(\log{\left(- \tan{\left(2 \right)} \right)} + i \pi\right)^{2} \sqrt[3]{\tan^{\operatorname{asin}{\left(x \right)}}{\left(2 \right)}} \sin{\left(\sqrt[3]{\tan^{\operatorname{asin}{\left(x \right)}}{\left(2 \right)}} \right)} \cos{\left(\sqrt[3]{\tan^{\operatorname{asin}{\left(x \right)}}{\left(2 \right)}} \right)}}{3 \left(x^{2} - 1\right)^{2}} + \frac{\left(\log{\left(- \tan{\left(2 \right)} \right)} + i \pi\right)^{3} \left(\tan^{\operatorname{asin}{\left(x \right)}}{\left(2 \right)}\right)^{\frac{2}{3}} \sin^{2}{\left(\sqrt[3]{\tan^{\operatorname{asin}{\left(x \right)}}{\left(2 \right)}} \right)}}{9 \left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{\left(\log{\left(- \tan{\left(2 \right)} \right)} + i \pi\right)^{3} \left(\tan^{\operatorname{asin}{\left(x \right)}}{\left(2 \right)}\right)^{\frac{2}{3}} \cos^{2}{\left(\sqrt[3]{\tan^{\operatorname{asin}{\left(x \right)}}{\left(2 \right)}} \right)}}{9 \left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{\left(\log{\left(- \tan{\left(2 \right)} \right)} + i \pi\right) \sqrt[3]{\tan^{\operatorname{asin}{\left(x \right)}}{\left(2 \right)}} \sin{\left(\sqrt[3]{\tan^{\operatorname{asin}{\left(x \right)}}{\left(2 \right)}} \right)} \cos{\left(\sqrt[3]{\tan^{\operatorname{asin}{\left(x \right)}}{\left(2 \right)}} \right)}}{3 \left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{\left(\log{\left(- \tan{\left(2 \right)} \right)} + i \pi\right)^{3} \sqrt[3]{\tan^{\operatorname{asin}{\left(x \right)}}{\left(2 \right)}} \sin{\left(\sqrt[3]{\tan^{\operatorname{asin}{\left(x \right)}}{\left(2 \right)}} \right)} \cos{\left(\sqrt[3]{\tan^{\operatorname{asin}{\left(x \right)}}{\left(2 \right)}} \right)}}{27 \left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{4 \left(\log{\left(- \tan{\left(2 \right)} \right)} + i \pi\right)^{3} \sin{\left(\sqrt[3]{\tan^{\operatorname{asin}{\left(x \right)}}{\left(2 \right)}} \right)} \cos{\left(\sqrt[3]{\tan^{\operatorname{asin}{\left(x \right)}}{\left(2 \right)}} \right)} \tan^{\operatorname{asin}{\left(x \right)}}{\left(2 \right)}}{27 \left(1 - x^{2}\right)^{\frac{3}{2}}}\right)
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Gráfico
Derivada de y=cos^2(cbrt(tg2^arcsinx))+exp^tg(x^2)
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