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y=(sin√7x)^tg9x
Derivada de la función/ y=(sin√7x)^tg9x

Derivada de y=(sin√7x)^tg9x

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
   tan(9*x)/  _____\
sin        \\/ 7*x /
sin⁡tan⁡(9x)(7x)\sin^{\tan{\left(9 x \right)}}{\left(\sqrt{7 x} \right)} 
sin(sqrt(7*x))^tan(9*x)
Solución detallada

  1. No logro encontrar los pasos en la búsqueda de esta derivada.

    Perola derivada

    (log⁡(tan⁡(9x))+1)tan⁡tan⁡(9x)(9x)\left(\log{\left(\tan{\left(9 x \right)} \right)} + 1\right) \tan^{\tan{\left(9 x \right)}}{\left(9 x \right)}

Respuesta:

(log⁡(tan⁡(9x))+1)tan⁡tan⁡(9x)(9x)\left(\log{\left(\tan{\left(9 x \right)} \right)} + 1\right) \tan^{\tan{\left(9 x \right)}}{\left(9 x \right)}

Gráfica
02468-8-6-4-2-1010-20002000
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Primera derivada [src] 
                     /                                        ___    /  _____\         \
   tan(9*x)/  _____\ |/         2     \    /   /  _____\\   \/ 7 *cos\\/ 7*x /*tan(9*x)|
sin        \\/ 7*x /*|\9 + 9*tan (9*x)/*log\sin\\/ 7*x // + ---------------------------|
                     |                                              ___    /  _____\   |
                     \                                          2*\/ x *sin\\/ 7*x /   /
((9tan⁡2(9x)+9)log⁡(sin⁡(7x))+7cos⁡(7x)tan⁡(9x)2xsin⁡(7x))sin⁡tan⁡(9x)(7x)\left(\left(9 \tan^{2}{\left(9 x \right)} + 9\right) \log{\left(\sin{\left(\sqrt{7 x} \right)} \right)} + \frac{\sqrt{7} \cos{\left(\sqrt{7 x} \right)} \tan{\left(9 x \right)}}{2 \sqrt{x} \sin{\left(\sqrt{7 x} \right)}}\right) \sin^{\tan{\left(9 x \right)}}{\left(\sqrt{7 x} \right)}
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Segunda derivada [src] 
                     /                                                                    2                                                                                                                                                              \
                     |/                                         ___    /  _____\         \                                                                                                                                                               |
                     ||   /       2     \    /   /  _____\\   \/ 7 *cos\\/ 7*x /*tan(9*x)|                                                                                                                                                               |
                     ||18*\1 + tan (9*x)/*log\sin\\/ 7*x // + ---------------------------|                                                                                                                                                               |
                     ||                                              ___    /  _____\    |                                                                       2/  _____\                ___ /       2     \    /  _____\     ___    /  _____\         |
   tan(9*x)/  _____\ |\                                            \/ x *sin\\/ 7*x /    /    7*tan(9*x)       /       2     \    /   /  _____\\            7*cos \\/ 7*x /*tan(9*x)   9*\/ 7 *\1 + tan (9*x)/*cos\\/ 7*x /   \/ 7 *cos\\/ 7*x /*tan(9*x)|
sin        \\/ 7*x /*|--------------------------------------------------------------------- - ---------- + 162*\1 + tan (9*x)/*log\sin\\/ 7*x //*tan(9*x) - ------------------------ + ------------------------------------ - ---------------------------|
                     |                                  4                                        4*x                                                                  2/  _____\                  ___    /  _____\                   3/2    /  _____\    |
                     \                                                                                                                                         4*x*sin \\/ 7*x /                \/ x *sin\\/ 7*x /                4*x   *sin\\/ 7*x /    /
((18(tan⁡2(9x)+1)log⁡(sin⁡(7x))+7cos⁡(7x)tan⁡(9x)xsin⁡(7x))24+162(tan⁡2(9x)+1)log⁡(sin⁡(7x))tan⁡(9x)−7tan⁡(9x)4x−7cos⁡2(7x)tan⁡(9x)4xsin⁡2(7x)+97(tan⁡2(9x)+1)cos⁡(7x)xsin⁡(7x)−7cos⁡(7x)tan⁡(9x)4x32sin⁡(7x))sin⁡tan⁡(9x)(7x)\left(\frac{\left(18 \left(\tan^{2}{\left(9 x \right)} + 1\right) \log{\left(\sin{\left(\sqrt{7 x} \right)} \right)} + \frac{\sqrt{7} \cos{\left(\sqrt{7 x} \right)} \tan{\left(9 x \right)}}{\sqrt{x} \sin{\left(\sqrt{7 x} \right)}}\right)^{2}}{4} + 162 \left(\tan^{2}{\left(9 x \right)} + 1\right) \log{\left(\sin{\left(\sqrt{7 x} \right)} \right)} \tan{\left(9 x \right)} - \frac{7 \tan{\left(9 x \right)}}{4 x} - \frac{7 \cos^{2}{\left(\sqrt{7 x} \right)} \tan{\left(9 x \right)}}{4 x \sin^{2}{\left(\sqrt{7 x} \right)}} + \frac{9 \sqrt{7} \left(\tan^{2}{\left(9 x \right)} + 1\right) \cos{\left(\sqrt{7 x} \right)}}{\sqrt{x} \sin{\left(\sqrt{7 x} \right)}} - \frac{\sqrt{7} \cos{\left(\sqrt{7 x} \right)} \tan{\left(9 x \right)}}{4 x^{\frac{3}{2}} \sin{\left(\sqrt{7 x} \right)}}\right) \sin^{\tan{\left(9 x \right)}}{\left(\sqrt{7 x} \right)}
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Tercera derivada [src] 
                     /                                                                    3                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    \
                     |/                                         ___    /  _____\         \                                                                      /                                         ___    /  _____\         \ /                                                                   2/  _____\              ___    /  _____\                 ___ /       2     \    /  _____\\                                                                                                                                                                                                                                                                                                                            |
                     ||   /       2     \    /   /  _____\\   \/ 7 *cos\\/ 7*x /*tan(9*x)|                                                                      |   /       2     \    /   /  _____\\   \/ 7 *cos\\/ 7*x /*tan(9*x)| |7*tan(9*x)       /       2     \    /   /  _____\\            7*cos \\/ 7*x /*tan(9*x)   \/ 7 *cos\\/ 7*x /*tan(9*x)   36*\/ 7 *\1 + tan (9*x)/*cos\\/ 7*x /|                                                                                                                                                                                                                                                                                                                            |
                     ||18*\1 + tan (9*x)/*log\sin\\/ 7*x // + ---------------------------|                                                                    3*|18*\1 + tan (9*x)/*log\sin\\/ 7*x // + ---------------------------|*|---------- - 648*\1 + tan (9*x)/*log\sin\\/ 7*x //*tan(9*x) + ------------------------ + --------------------------- - -------------------------------------|                                                                                                                                                                                                                                                                                                                            |
                     ||                                              ___    /  _____\    |                        2                         /       2     \     |                                              ___    /  _____\    | |    x                                                                  2/  _____\              3/2    /  _____\                    ___    /  _____\         |                                                                           2/  _____\ /       2     \         2/  _____\                 ___ /       2     \    /  _____\       ___    /  _____\                ___    3/  _____\                ___    /  _____\                  ___ /       2     \    /  _____\         |
   tan(9*x)/  _____\ |\                                            \/ x *sin\\/ 7*x /    /         /       2     \     /   /  _____\\   189*\1 + tan (9*x)/     \                                            \/ x *sin\\/ 7*x /    / \                                                                  x*sin \\/ 7*x /             x   *sin\\/ 7*x /                  \/ x *sin\\/ 7*x /         /   21*tan(9*x)           2      /       2     \    /   /  _____\\   189*cos \\/ 7*x /*\1 + tan (9*x)/   21*cos \\/ 7*x /*tan(9*x)   27*\/ 7 *\1 + tan (9*x)/*cos\\/ 7*x /   3*\/ 7 *cos\\/ 7*x /*tan(9*x)   7*\/ 7 *cos \\/ 7*x /*tan(9*x)   7*\/ 7 *cos\\/ 7*x /*tan(9*x)   243*\/ 7 *\1 + tan (9*x)/*cos\\/ 7*x /*tan(9*x)|
sin        \\/ 7*x /*|--------------------------------------------------------------------- + 1458*\1 + tan (9*x)/ *log\sin\\/ 7*x // - ------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------- + 2916*tan (9*x)*\1 + tan (9*x)/*log\sin\\/ 7*x // - --------------------------------- + ------------------------- - ------------------------------------- + ----------------------------- + ------------------------------ + ----------------------------- + -----------------------------------------------|
                     |                                  8                                                                                       4*x                                                                                                                             8                                                                                                                            2                                                                        2/  _____\                  2    2/  _____\                  3/2    /  _____\                    5/2    /  _____\                3/2    3/  _____\                3/2    /  _____\                         ___    /  _____\              |
                     \                                                                                                                                                                                                                                                                                                                                                                                    8*x                                                                  4*x*sin \\/ 7*x /               8*x *sin \\/ 7*x /               4*x   *sin\\/ 7*x /                 8*x   *sin\\/ 7*x /             4*x   *sin \\/ 7*x /             4*x   *sin\\/ 7*x /                       \/ x *sin\\/ 7*x /              /
((18(tan⁡2(9x)+1)log⁡(sin⁡(7x))+7cos⁡(7x)tan⁡(9x)xsin⁡(7x))38−3(18(tan⁡2(9x)+1)log⁡(sin⁡(7x))+7cos⁡(7x)tan⁡(9x)xsin⁡(7x))(−648(tan⁡2(9x)+1)log⁡(sin⁡(7x))tan⁡(9x)+7tan⁡(9x)x+7cos⁡2(7x)tan⁡(9x)xsin⁡2(7x)−367(tan⁡2(9x)+1)cos⁡(7x)xsin⁡(7x)+7cos⁡(7x)tan⁡(9x)x32sin⁡(7x))8+1458(tan⁡2(9x)+1)2log⁡(sin⁡(7x))+2916(tan⁡2(9x)+1)log⁡(sin⁡(7x))tan⁡2(9x)−189(tan⁡2(9x)+1)4x−189(tan⁡2(9x)+1)cos⁡2(7x)4xsin⁡2(7x)+21tan⁡(9x)8x2+21cos⁡2(7x)tan⁡(9x)8x2sin⁡2(7x)+2437(tan⁡2(9x)+1)cos⁡(7x)tan⁡(9x)xsin⁡(7x)−277(tan⁡2(9x)+1)cos⁡(7x)4x32sin⁡(7x)+77cos⁡(7x)tan⁡(9x)4x32sin⁡(7x)+77cos⁡3(7x)tan⁡(9x)4x32sin⁡3(7x)+37cos⁡(7x)tan⁡(9x)8x52sin⁡(7x))sin⁡tan⁡(9x)(7x)\left(\frac{\left(18 \left(\tan^{2}{\left(9 x \right)} + 1\right) \log{\left(\sin{\left(\sqrt{7 x} \right)} \right)} + \frac{\sqrt{7} \cos{\left(\sqrt{7 x} \right)} \tan{\left(9 x \right)}}{\sqrt{x} \sin{\left(\sqrt{7 x} \right)}}\right)^{3}}{8} - \frac{3 \left(18 \left(\tan^{2}{\left(9 x \right)} + 1\right) \log{\left(\sin{\left(\sqrt{7 x} \right)} \right)} + \frac{\sqrt{7} \cos{\left(\sqrt{7 x} \right)} \tan{\left(9 x \right)}}{\sqrt{x} \sin{\left(\sqrt{7 x} \right)}}\right) \left(- 648 \left(\tan^{2}{\left(9 x \right)} + 1\right) \log{\left(\sin{\left(\sqrt{7 x} \right)} \right)} \tan{\left(9 x \right)} + \frac{7 \tan{\left(9 x \right)}}{x} + \frac{7 \cos^{2}{\left(\sqrt{7 x} \right)} \tan{\left(9 x \right)}}{x \sin^{2}{\left(\sqrt{7 x} \right)}} - \frac{36 \sqrt{7} \left(\tan^{2}{\left(9 x \right)} + 1\right) \cos{\left(\sqrt{7 x} \right)}}{\sqrt{x} \sin{\left(\sqrt{7 x} \right)}} + \frac{\sqrt{7} \cos{\left(\sqrt{7 x} \right)} \tan{\left(9 x \right)}}{x^{\frac{3}{2}} \sin{\left(\sqrt{7 x} \right)}}\right)}{8} + 1458 \left(\tan^{2}{\left(9 x \right)} + 1\right)^{2} \log{\left(\sin{\left(\sqrt{7 x} \right)} \right)} + 2916 \left(\tan^{2}{\left(9 x \right)} + 1\right) \log{\left(\sin{\left(\sqrt{7 x} \right)} \right)} \tan^{2}{\left(9 x \right)} - \frac{189 \left(\tan^{2}{\left(9 x \right)} + 1\right)}{4 x} - \frac{189 \left(\tan^{2}{\left(9 x \right)} + 1\right) \cos^{2}{\left(\sqrt{7 x} \right)}}{4 x \sin^{2}{\left(\sqrt{7 x} \right)}} + \frac{21 \tan{\left(9 x \right)}}{8 x^{2}} + \frac{21 \cos^{2}{\left(\sqrt{7 x} \right)} \tan{\left(9 x \right)}}{8 x^{2} \sin^{2}{\left(\sqrt{7 x} \right)}} + \frac{243 \sqrt{7} \left(\tan^{2}{\left(9 x \right)} + 1\right) \cos{\left(\sqrt{7 x} \right)} \tan{\left(9 x \right)}}{\sqrt{x} \sin{\left(\sqrt{7 x} \right)}} - \frac{27 \sqrt{7} \left(\tan^{2}{\left(9 x \right)} + 1\right) \cos{\left(\sqrt{7 x} \right)}}{4 x^{\frac{3}{2}} \sin{\left(\sqrt{7 x} \right)}} + \frac{7 \sqrt{7} \cos{\left(\sqrt{7 x} \right)} \tan{\left(9 x \right)}}{4 x^{\frac{3}{2}} \sin{\left(\sqrt{7 x} \right)}} + \frac{7 \sqrt{7} \cos^{3}{\left(\sqrt{7 x} \right)} \tan{\left(9 x \right)}}{4 x^{\frac{3}{2}} \sin^{3}{\left(\sqrt{7 x} \right)}} + \frac{3 \sqrt{7} \cos{\left(\sqrt{7 x} \right)} \tan{\left(9 x \right)}}{8 x^{\frac{5}{2}} \sin{\left(\sqrt{7 x} \right)}}\right) \sin^{\tan{\left(9 x \right)}}{\left(\sqrt{7 x} \right)}
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Gráfico
Derivada de y=(sin√7x)^tg9x
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