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y=arcsin(tg(2)^(cos(lnx)))
Derivada de la función/ cos(lnx)/ arcsin/ y=arcsin(tg(2)^(cos(lnx)))

Derivada de y=arcsin(tg(2)^(cos(lnx)))

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
    /   cos(log(x))   \
asin\tan           (2)/
asin⁡(tan⁡cos⁡(log⁡(x))(2))\operatorname{asin}{\left(\tan^{\cos{\left(\log{\left(x \right)} \right)}}{\left(2 \right)} \right)} 
asin(tan(2)^cos(log(x)))
Gráfica
02468-8-6-4-2-10100.02-0.02
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
    cos(log(x))                                      
-tan           (2)*(pi*I + log(-tan(2)))*sin(log(x)) 
-----------------------------------------------------
                 _________________________           
                /        2*cos(log(x))               
            x*\/  1 - tan             (2)
−(log⁡(−tan⁡(2))+iπ)sin⁡(log⁡(x))tan⁡cos⁡(log⁡(x))(2)x1−tan⁡2cos⁡(log⁡(x))(2)- \frac{\left(\log{\left(- \tan{\left(2 \right)} \right)} + i \pi\right) \sin{\left(\log{\left(x \right)} \right)} \tan^{\cos{\left(\log{\left(x \right)} \right)}}{\left(2 \right)}}{x \sqrt{1 - \tan^{2 \cos{\left(\log{\left(x \right)} \right)}}{\left(2 \right)}}}
Simplificar
Segunda derivada [src] 
                                        /                                                       2            2*cos(log(x))                                       \
   cos(log(x))                          |                  2                                 sin (log(x))*tan             (2)*(pi*I + log(-tan(2)))              |
tan           (2)*(pi*I + log(-tan(2)))*|-cos(log(x)) + sin (log(x))*(pi*I + log(-tan(2))) + ------------------------------------------------------ + sin(log(x))|
                                        |                                                                          2*cos(log(x))                                 |
                                        \                                                                   1 - tan             (2)                              /
------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                       _________________________                                                                  
                                                                  2   /        2*cos(log(x))                                                                      
                                                                 x *\/  1 - tan             (2)
(log⁡(−tan⁡(2))+iπ)((log⁡(−tan⁡(2))+iπ)sin⁡2(log⁡(x))+sin⁡(log⁡(x))−cos⁡(log⁡(x))+(log⁡(−tan⁡(2))+iπ)sin⁡2(log⁡(x))tan⁡2cos⁡(log⁡(x))(2)1−tan⁡2cos⁡(log⁡(x))(2))tan⁡cos⁡(log⁡(x))(2)x21−tan⁡2cos⁡(log⁡(x))(2)\frac{\left(\log{\left(- \tan{\left(2 \right)} \right)} + i \pi\right) \left(\left(\log{\left(- \tan{\left(2 \right)} \right)} + i \pi\right) \sin^{2}{\left(\log{\left(x \right)} \right)} + \sin{\left(\log{\left(x \right)} \right)} - \cos{\left(\log{\left(x \right)} \right)} + \frac{\left(\log{\left(- \tan{\left(2 \right)} \right)} + i \pi\right) \sin^{2}{\left(\log{\left(x \right)} \right)} \tan^{2 \cos{\left(\log{\left(x \right)} \right)}}{\left(2 \right)}}{1 - \tan^{2 \cos{\left(\log{\left(x \right)} \right)}}{\left(2 \right)}}\right) \tan^{\cos{\left(\log{\left(x \right)} \right)}}{\left(2 \right)}}{x^{2} \sqrt{1 - \tan^{2 \cos{\left(\log{\left(x \right)} \right)}}{\left(2 \right)}}}
Simplificar
Tercera derivada [src] 
                                        /                                                                                                                                                                                     2    3            2*cos(log(x))           2            2*cos(log(x))                                                   2    3            4*cos(log(x))           2*cos(log(x))                                                 \
   cos(log(x))                          |                                                    2    3                2                                                                                   4*(pi*I + log(-tan(2))) *sin (log(x))*tan             (2)   3*sin (log(x))*tan             (2)*(pi*I + log(-tan(2)))   3*(pi*I + log(-tan(2))) *sin (log(x))*tan             (2)   3*tan             (2)*(pi*I + log(-tan(2)))*cos(log(x))*sin(log(x))|
tan           (2)*(pi*I + log(-tan(2)))*|-sin(log(x)) + 3*cos(log(x)) - (pi*I + log(-tan(2))) *sin (log(x)) - 3*sin (log(x))*(pi*I + log(-tan(2))) + 3*(pi*I + log(-tan(2)))*cos(log(x))*sin(log(x)) - --------------------------------------------------------- - -------------------------------------------------------- - --------------------------------------------------------- + -------------------------------------------------------------------|
                                        |                                                                                                                                                                                      2*cos(log(x))                                              2*cos(log(x))                                                                2                                               2*cos(log(x))                         |
                                        |                                                                                                                                                                               1 - tan             (2)                                    1 - tan             (2)                                    /       2*cos(log(x))   \                                         1 - tan             (2)                      |
                                        \                                                                                                                                                                                                                                                                                                     \1 - tan             (2)/                                                                                      /
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                                                     _________________________                                                                                                                                                                                                                
                                                                                                                                                                                                                3   /        2*cos(log(x))                                                                                                                                                                                                                    
                                                                                                                                                                                                               x *\/  1 - tan             (2)
(log⁡(−tan⁡(2))+iπ)(−(log⁡(−tan⁡(2))+iπ)2sin⁡3(log⁡(x))−3(log⁡(−tan⁡(2))+iπ)sin⁡2(log⁡(x))+3(log⁡(−tan⁡(2))+iπ)sin⁡(log⁡(x))cos⁡(log⁡(x))−sin⁡(log⁡(x))+3cos⁡(log⁡(x))−4(log⁡(−tan⁡(2))+iπ)2sin⁡3(log⁡(x))tan⁡2cos⁡(log⁡(x))(2)1−tan⁡2cos⁡(log⁡(x))(2)−3(log⁡(−tan⁡(2))+iπ)sin⁡2(log⁡(x))tan⁡2cos⁡(log⁡(x))(2)1−tan⁡2cos⁡(log⁡(x))(2)+3(log⁡(−tan⁡(2))+iπ)sin⁡(log⁡(x))cos⁡(log⁡(x))tan⁡2cos⁡(log⁡(x))(2)1−tan⁡2cos⁡(log⁡(x))(2)−3(log⁡(−tan⁡(2))+iπ)2sin⁡3(log⁡(x))tan⁡4cos⁡(log⁡(x))(2)(1−tan⁡2cos⁡(log⁡(x))(2))2)tan⁡cos⁡(log⁡(x))(2)x31−tan⁡2cos⁡(log⁡(x))(2)\frac{\left(\log{\left(- \tan{\left(2 \right)} \right)} + i \pi\right) \left(- \left(\log{\left(- \tan{\left(2 \right)} \right)} + i \pi\right)^{2} \sin^{3}{\left(\log{\left(x \right)} \right)} - 3 \left(\log{\left(- \tan{\left(2 \right)} \right)} + i \pi\right) \sin^{2}{\left(\log{\left(x \right)} \right)} + 3 \left(\log{\left(- \tan{\left(2 \right)} \right)} + i \pi\right) \sin{\left(\log{\left(x \right)} \right)} \cos{\left(\log{\left(x \right)} \right)} - \sin{\left(\log{\left(x \right)} \right)} + 3 \cos{\left(\log{\left(x \right)} \right)} - \frac{4 \left(\log{\left(- \tan{\left(2 \right)} \right)} + i \pi\right)^{2} \sin^{3}{\left(\log{\left(x \right)} \right)} \tan^{2 \cos{\left(\log{\left(x \right)} \right)}}{\left(2 \right)}}{1 - \tan^{2 \cos{\left(\log{\left(x \right)} \right)}}{\left(2 \right)}} - \frac{3 \left(\log{\left(- \tan{\left(2 \right)} \right)} + i \pi\right) \sin^{2}{\left(\log{\left(x \right)} \right)} \tan^{2 \cos{\left(\log{\left(x \right)} \right)}}{\left(2 \right)}}{1 - \tan^{2 \cos{\left(\log{\left(x \right)} \right)}}{\left(2 \right)}} + \frac{3 \left(\log{\left(- \tan{\left(2 \right)} \right)} + i \pi\right) \sin{\left(\log{\left(x \right)} \right)} \cos{\left(\log{\left(x \right)} \right)} \tan^{2 \cos{\left(\log{\left(x \right)} \right)}}{\left(2 \right)}}{1 - \tan^{2 \cos{\left(\log{\left(x \right)} \right)}}{\left(2 \right)}} - \frac{3 \left(\log{\left(- \tan{\left(2 \right)} \right)} + i \pi\right)^{2} \sin^{3}{\left(\log{\left(x \right)} \right)} \tan^{4 \cos{\left(\log{\left(x \right)} \right)}}{\left(2 \right)}}{\left(1 - \tan^{2 \cos{\left(\log{\left(x \right)} \right)}}{\left(2 \right)}\right)^{2}}\right) \tan^{\cos{\left(\log{\left(x \right)} \right)}}{\left(2 \right)}}{x^{3} \sqrt{1 - \tan^{2 \cos{\left(\log{\left(x \right)} \right)}}{\left(2 \right)}}}
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Gráfico
Derivada de y=arcsin(tg(2)^(cos(lnx)))
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