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y=sin(x^(-1\3)-arctg(2x))
Derivada de la función/ arctg/ y=sin/ tg(2x)/ y=sin(x^(-1\3)-arctg(2x))

Derivada de y=sin(x^(-1\3)-arctg(2x))

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

Ha introducido [src] 
   /  1              \
sin|----- - atan(2*x)|
   |3 ___            |
   \\/ x             /
sin⁡(−atan⁡(2x)+1x3)\sin{\left(- \operatorname{atan}{\left(2 x \right)} + \frac{1}{\sqrt[3]{x}} \right)} 
sin(x^(-1/3) - atan(2*x))
Gráfica
02468-8-6-4-2-10105-5
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Trazar el gráfico f'(x)
Primera derivada [src] 
/     2         1   \    /    1              \
|- -------- - ------|*cos|- ----- + atan(2*x)|
|         2      4/3|    |  3 ___            |
\  1 + 4*x    3*x   /    \  \/ x             /
(−24x2+1−13x43)cos⁡(atan⁡(2x)−1x3)\left(- \frac{2}{4 x^{2} + 1} - \frac{1}{3 x^{\frac{4}{3}}}\right) \cos{\left(\operatorname{atan}{\left(2 x \right)} - \frac{1}{\sqrt[3]{x}} \right)}
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Segunda derivada [src] 
                 2                                                                           
/ 1        6    \     /    1              \     / 1         36*x   \    /    1              \
|---- + --------| *sin|- ----- + atan(2*x)| + 4*|---- + -----------|*cos|- ----- + atan(2*x)|
| 4/3          2|     |  3 ___            |     | 7/3             2|    |  3 ___            |
\x      1 + 4*x /     \  \/ x             /     |x      /       2\ |    \  \/ x             /
                                                \       \1 + 4*x / /                         
---------------------------------------------------------------------------------------------
                                              9
4(36x(4x2+1)2+1x73)cos⁡(atan⁡(2x)−1x3)+(64x2+1+1x43)2sin⁡(atan⁡(2x)−1x3)9\frac{4 \left(\frac{36 x}{\left(4 x^{2} + 1\right)^{2}} + \frac{1}{x^{\frac{7}{3}}}\right) \cos{\left(\operatorname{atan}{\left(2 x \right)} - \frac{1}{\sqrt[3]{x}} \right)} + \left(\frac{6}{4 x^{2} + 1} + \frac{1}{x^{\frac{4}{3}}}\right)^{2} \sin{\left(\operatorname{atan}{\left(2 x \right)} - \frac{1}{\sqrt[3]{x}} \right)}}{9}
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Tercera derivada [src] 
                 3                              /                                2  \                                                                                              
/ 1        6    \     /    1              \     |      108         7       1728*x   |    /    1              \      / 1         36*x   \ / 1        6    \    /    1              \
|---- + --------| *cos|- ----- + atan(2*x)| - 4*|- ----------- + ----- + -----------|*cos|- ----- + atan(2*x)| - 12*|---- + -----------|*|---- + --------|*sin|- ----- + atan(2*x)|
| 4/3          2|     |  3 ___            |     |            2    10/3             3|    |  3 ___            |      | 7/3             2| | 4/3          2|    |  3 ___            |
\x      1 + 4*x /     \  \/ x             /     |  /       2\    x       /       2\ |    \  \/ x             /      |x      /       2\ | \x      1 + 4*x /    \  \/ x             /
                                                \  \1 + 4*x /            \1 + 4*x / /                               \       \1 + 4*x / /                                           
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                                                                                         27
−12(36x(4x2+1)2+1x73)(64x2+1+1x43)sin⁡(atan⁡(2x)−1x3)+(64x2+1+1x43)3cos⁡(atan⁡(2x)−1x3)−4(1728x2(4x2+1)3−108(4x2+1)2+7x103)cos⁡(atan⁡(2x)−1x3)27\frac{- 12 \left(\frac{36 x}{\left(4 x^{2} + 1\right)^{2}} + \frac{1}{x^{\frac{7}{3}}}\right) \left(\frac{6}{4 x^{2} + 1} + \frac{1}{x^{\frac{4}{3}}}\right) \sin{\left(\operatorname{atan}{\left(2 x \right)} - \frac{1}{\sqrt[3]{x}} \right)} + \left(\frac{6}{4 x^{2} + 1} + \frac{1}{x^{\frac{4}{3}}}\right)^{3} \cos{\left(\operatorname{atan}{\left(2 x \right)} - \frac{1}{\sqrt[3]{x}} \right)} - 4 \left(\frac{1728 x^{2}}{\left(4 x^{2} + 1\right)^{3}} - \frac{108}{\left(4 x^{2} + 1\right)^{2}} + \frac{7}{x^{\frac{10}{3}}}\right) \cos{\left(\operatorname{atan}{\left(2 x \right)} - \frac{1}{\sqrt[3]{x}} \right)}}{27}
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Gráfico
Derivada de y=sin(x^(-1\3)-arctg(2x))
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