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y=exp(arctgsqrt(2x^3+5))
Derivada de la función/ arctg/ y=exp(arctgsqrt(2x^3+5))

Derivada de y=exp(arctgsqrt(2x^3+5))

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
     /   __________\
     |  /    3     |
 atan\\/  2*x  + 5 /
e
eatan⁡(2x3+5)e^{\operatorname{atan}{\left(\sqrt{2 x^{3} + 5} \right)}} 
exp(atan(sqrt(2*x^3 + 5)))
Gráfica
02468-8-6-4-2-1010010
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
          /   __________\
          |  /    3     |
   2  atan\\/  2*x  + 5 /
3*x *e                   
-------------------------
               __________
 /       3\   /    3     
 \6 + 2*x /*\/  2*x  + 5
3x2eatan⁡(2x3+5)2x3+5(2x3+6)\frac{3 x^{2} e^{\operatorname{atan}{\left(\sqrt{2 x^{3} + 5} \right)}}}{\sqrt{2 x^{3} + 5} \left(2 x^{3} + 6\right)}
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Segunda derivada [src] 
                                                                                              /   __________\
    /                         3                     3                         3        \      |  /        3 |
    |      1               3*x                   3*x                       3*x         |  atan\\/  5 + 2*x  /
3*x*|------------- - --------------- - ------------------------ + ---------------------|*e                   
    |   __________               3/2                 __________     /     3\ /       3\|                     
    |  /        3      /       3\        /     3\   /        3    4*\3 + x /*\5 + 2*x /|                     
    \\/  5 + 2*x     2*\5 + 2*x /      2*\3 + x /*\/  5 + 2*x                          /                     
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                                                         3                                                   
                                                    3 + x
3x(−3x32(2x3+5)32+3x34(x3+3)(2x3+5)−3x32(x3+3)2x3+5+12x3+5)eatan⁡(2x3+5)x3+3\frac{3 x \left(- \frac{3 x^{3}}{2 \left(2 x^{3} + 5\right)^{\frac{3}{2}}} + \frac{3 x^{3}}{4 \left(x^{3} + 3\right) \left(2 x^{3} + 5\right)} - \frac{3 x^{3}}{2 \left(x^{3} + 3\right) \sqrt{2 x^{3} + 5}} + \frac{1}{\sqrt{2 x^{3} + 5}}\right) e^{\operatorname{atan}{\left(\sqrt{2 x^{3} + 5} \right)}}}{x^{3} + 3}
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Tercera derivada [src] 
                                                                                                                                                                                                                                           /   __________\
  /                        3                6                    3                        6                         6                        6                        6                        3                         6          \      |  /        3 |
  |      1              9*x             27*x                  9*x                      9*x                       9*x                     27*x                     27*x                      9*x                       9*x           |  atan\\/  5 + 2*x  /
3*|------------- - ------------- + --------------- - ---------------------- + ---------------------- + ----------------------- - ---------------------- - ---------------------- + --------------------- + -------------------------|*e                   
  |   __________             3/2               5/2               __________                      3/2           2    __________                        2             2                /     3\ /       3\             2           3/2|                     
  |  /        3    /       3\        /       3\      /     3\   /        3    /     3\ /       3\      /     3\    /        3      /     3\ /       3\      /     3\  /       3\   2*\3 + x /*\5 + 2*x /     /     3\  /       3\   |                     
  \\/  5 + 2*x     \5 + 2*x /      2*\5 + 2*x /      \3 + x /*\/  5 + 2*x     \3 + x /*\5 + 2*x /      \3 + x / *\/  5 + 2*x     4*\3 + x /*\5 + 2*x /    4*\3 + x / *\5 + 2*x /                           8*\3 + x / *\5 + 2*x /   /                     
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                                                                                                                               3                                                                                                                          
                                                                                                                          3 + x
3(27x62(2x3+5)52−27x64(x3+3)(2x3+5)2+9x6(x3+3)(2x3+5)32−27x64(x3+3)2(2x3+5)+9x6(x3+3)22x3+5+9x68(x3+3)2(2x3+5)32−9x3(2x3+5)32+9x32(x3+3)(2x3+5)−9x3(x3+3)2x3+5+12x3+5)eatan⁡(2x3+5)x3+3\frac{3 \left(\frac{27 x^{6}}{2 \left(2 x^{3} + 5\right)^{\frac{5}{2}}} - \frac{27 x^{6}}{4 \left(x^{3} + 3\right) \left(2 x^{3} + 5\right)^{2}} + \frac{9 x^{6}}{\left(x^{3} + 3\right) \left(2 x^{3} + 5\right)^{\frac{3}{2}}} - \frac{27 x^{6}}{4 \left(x^{3} + 3\right)^{2} \left(2 x^{3} + 5\right)} + \frac{9 x^{6}}{\left(x^{3} + 3\right)^{2} \sqrt{2 x^{3} + 5}} + \frac{9 x^{6}}{8 \left(x^{3} + 3\right)^{2} \left(2 x^{3} + 5\right)^{\frac{3}{2}}} - \frac{9 x^{3}}{\left(2 x^{3} + 5\right)^{\frac{3}{2}}} + \frac{9 x^{3}}{2 \left(x^{3} + 3\right) \left(2 x^{3} + 5\right)} - \frac{9 x^{3}}{\left(x^{3} + 3\right) \sqrt{2 x^{3} + 5}} + \frac{1}{\sqrt{2 x^{3} + 5}}\right) e^{\operatorname{atan}{\left(\sqrt{2 x^{3} + 5} \right)}}}{x^{3} + 3}
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Gráfico
Derivada de y=exp(arctgsqrt(2x^3+5))
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