Sr Examen

Derivada de y=x^4arctg3x

Función f() - derivada -er orden en el punto
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Gráfico:

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Solución

Ha introducido [src]
 4          
x *atan(3*x)
$$x^{4} \operatorname{atan}{\left(3 x \right)}$$
x^4*atan(3*x)
Gráfica
Primera derivada [src]
     4                   
  3*x         3          
-------- + 4*x *atan(3*x)
       2                 
1 + 9*x                  
$$\frac{3 x^{4}}{9 x^{2} + 1} + 4 x^{3} \operatorname{atan}{\left(3 x \right)}$$
Segunda derivada [src]
     /                     3              \
   2 |                  9*x         4*x   |
6*x *|2*atan(3*x) - ----------- + --------|
     |                        2          2|
     |              /       2\    1 + 9*x |
     \              \1 + 9*x /            /
$$6 x^{2} \left(- \frac{9 x^{3}}{\left(9 x^{2} + 1\right)^{2}} + \frac{4 x}{9 x^{2} + 1} + 2 \operatorname{atan}{\left(3 x \right)}\right)$$
Tercera derivada [src]
    /                                            /          2  \\
    |                                          3 |      36*x   ||
    |                                       9*x *|-1 + --------||
    |                      3                     |            2||
    |                 108*x        18*x          \     1 + 9*x /|
6*x*|4*atan(3*x) - ----------- + -------- + --------------------|
    |                        2          2                 2     |
    |              /       2\    1 + 9*x        /       2\      |
    \              \1 + 9*x /                   \1 + 9*x /      /
$$6 x \left(\frac{9 x^{3} \left(\frac{36 x^{2}}{9 x^{2} + 1} - 1\right)}{\left(9 x^{2} + 1\right)^{2}} - \frac{108 x^{3}}{\left(9 x^{2} + 1\right)^{2}} + \frac{18 x}{9 x^{2} + 1} + 4 \operatorname{atan}{\left(3 x \right)}\right)$$
Gráfico
Derivada de y=x^4arctg3x