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x^(sin7)*arctg(sqrt(2x))
Derivada de la función/ sqrt(2x)/ arctg/ x^(sin7)*arctg(sqrt(2x))

Derivada de x^(sin7)*arctg(sqrt(2x))

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

Gráfico:

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Solución

Ha introducido [src] 
 sin(7)     /  _____\
x      *atan\\/ 2*x /
xsin⁡(7)atan⁡(2x)x^{\sin{\left(7 \right)}} \operatorname{atan}{\left(\sqrt{2 x} \right)} 
x^sin(7)*atan(sqrt(2*x))
Gráfica
02468-8-6-4-2-1010010
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Primera derivada [src] 
 sin(7)     /  _____\              ___  sin(7)  
x      *atan\\/ 2*x /*sin(7)     \/ 2 *x        
---------------------------- + -----------------
             x                     ___          
                               2*\/ x *(1 + 2*x)
xsin⁡(7)sin⁡(7)atan⁡(2x)x+2xsin⁡(7)2x(2x+1)\frac{x^{\sin{\left(7 \right)}} \sin{\left(7 \right)} \operatorname{atan}{\left(\sqrt{2 x} \right)}}{x} + \frac{\sqrt{2} x^{\sin{\left(7 \right)}}}{2 \sqrt{x} \left(2 x + 1\right)}
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Segunda derivada [src] 
        /                                                       ___ /1      4   \\
        |   ___                            /  _____\          \/ 2 *|- + -------||
 sin(7) | \/ 2 *sin(7)    (1 - sin(7))*atan\\/ 2*x /*sin(7)         \x   1 + 2*x/|
x      *|-------------- - --------------------------------- - -------------------|
        | 3/2                              2                       ___           |
        \x   *(1 + 2*x)                   x                    4*\/ x *(1 + 2*x) /
xsin⁡(7)(−(1−sin⁡(7))sin⁡(7)atan⁡(2x)x2−2(42x+1+1x)4x(2x+1)+2sin⁡(7)x32(2x+1))x^{\sin{\left(7 \right)}} \left(- \frac{\left(1 - \sin{\left(7 \right)}\right) \sin{\left(7 \right)} \operatorname{atan}{\left(\sqrt{2 x} \right)}}{x^{2}} - \frac{\sqrt{2} \left(\frac{4}{2 x + 1} + \frac{1}{x}\right)}{4 \sqrt{x} \left(2 x + 1\right)} + \frac{\sqrt{2} \sin{\left(7 \right)}}{x^{\frac{3}{2}} \left(2 x + 1\right)}\right)
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Tercera derivada [src] 
        /                                                  ___ /3        32            8     \                                                             \
        |                                                \/ 2 *|-- + ---------- + -----------|                                     ___ /1      4   \       |
        |/       2              \     /  _____\                | 2            2   x*(1 + 2*x)|       ___                       3*\/ 2 *|- + -------|*sin(7)|
 sin(7) |\2 + sin (7) - 3*sin(7)/*atan\\/ 2*x /*sin(7)         \x    (1 + 2*x)               /   3*\/ 2 *(1 - sin(7))*sin(7)           \x   1 + 2*x/       |
x      *|--------------------------------------------- + ------------------------------------- - --------------------------- - ----------------------------|
        |                       3                                      ___                                5/2                           3/2                |
        \                      x                                   8*\/ x *(1 + 2*x)                   2*x   *(1 + 2*x)              4*x   *(1 + 2*x)      /
xsin⁡(7)((−3sin⁡(7)+sin⁡2(7)+2)sin⁡(7)atan⁡(2x)x3+2(32(2x+1)2+8x(2x+1)+3x2)8x(2x+1)−32(42x+1+1x)sin⁡(7)4x32(2x+1)−32(1−sin⁡(7))sin⁡(7)2x52(2x+1))x^{\sin{\left(7 \right)}} \left(\frac{\left(- 3 \sin{\left(7 \right)} + \sin^{2}{\left(7 \right)} + 2\right) \sin{\left(7 \right)} \operatorname{atan}{\left(\sqrt{2 x} \right)}}{x^{3}} + \frac{\sqrt{2} \left(\frac{32}{\left(2 x + 1\right)^{2}} + \frac{8}{x \left(2 x + 1\right)} + \frac{3}{x^{2}}\right)}{8 \sqrt{x} \left(2 x + 1\right)} - \frac{3 \sqrt{2} \left(\frac{4}{2 x + 1} + \frac{1}{x}\right) \sin{\left(7 \right)}}{4 x^{\frac{3}{2}} \left(2 x + 1\right)} - \frac{3 \sqrt{2} \left(1 - \sin{\left(7 \right)}\right) \sin{\left(7 \right)}}{2 x^{\frac{5}{2}} \left(2 x + 1\right)}\right)
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Gráfico
Derivada de x^(sin7)*arctg(sqrt(2x))
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