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y=(2x^3+5)arctan(x^2-1)
Derivada de la función/ x^2-1/ y=(2x^3+5)/ arctan/ y=(2x^3+5)arctan(x^2-1)

Derivada de y=(2x^3+5)arctan(x^2-1)

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

Ha introducido [src] 
/   3    \     / 2    \
\2*x  + 5/*atan\x  - 1/
(2x3+5)atan⁡(x2−1)\left(2 x^{3} + 5\right) \operatorname{atan}{\left(x^{2} - 1 \right)} 
(2*x^3 + 5)*atan(x^2 - 1)
Gráfica
02468-8-6-4-2-1010-50005000
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Primera derivada [src] 
                        /   3    \
   2     / 2    \   2*x*\2*x  + 5/
6*x *atan\x  - 1/ + --------------
                                2 
                        / 2    \  
                    1 + \x  - 1/
6x2atan⁡(x2−1)+2x(2x3+5)(x2−1)2+16 x^{2} \operatorname{atan}{\left(x^{2} - 1 \right)} + \frac{2 x \left(2 x^{3} + 5\right)}{\left(x^{2} - 1\right)^{2} + 1}
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Segunda derivada [src] 
  /                                     /        2 /      2\\           \
  |                                     |     4*x *\-1 + x /| /       3\|
  |                                     |-1 + --------------|*\5 + 2*x /|
  |                                     |                  2|           |
  |                            3        |         /      2\ |           |
  |        /      2\       12*x         \     1 + \-1 + x / /           |
2*|6*x*atan\-1 + x / + -------------- - --------------------------------|
  |                                 2                         2         |
  |                        /      2\                 /      2\          |
  \                    1 + \-1 + x /             1 + \-1 + x /          /
2(12x3(x2−1)2+1+6xatan⁡(x2−1)−(2x3+5)(4x2(x2−1)(x2−1)2+1−1)(x2−1)2+1)2 \left(\frac{12 x^{3}}{\left(x^{2} - 1\right)^{2} + 1} + 6 x \operatorname{atan}{\left(x^{2} - 1 \right)} - \frac{\left(2 x^{3} + 5\right) \left(\frac{4 x^{2} \left(x^{2} - 1\right)}{\left(x^{2} - 1\right)^{2} + 1} - 1\right)}{\left(x^{2} - 1\right)^{2} + 1}\right)
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Tercera derivada [src] 
  /                                                                               /                         2\\
  |                                        /        2 /      2\\                  |              2 /      2\ ||
  |                                      2 |     4*x *\-1 + x /|       /       3\ |       2   8*x *\-1 + x / ||
  |                                   9*x *|-1 + --------------|   2*x*\5 + 2*x /*|3 - 5*x  + ---------------||
  |                                        |                  2|                  |                         2||
  |                          2             |         /      2\ |                  |                /      2\ ||
  |      /      2\       18*x              \     1 + \-1 + x / /                  \            1 + \-1 + x / /|
4*|3*atan\-1 + x / + -------------- - -------------------------- + -------------------------------------------|
  |                               2                      2                                      2             |
  |                      /      2\              /      2\                       /             2\              |
  |                  1 + \-1 + x /          1 + \-1 + x /                       |    /      2\ |              |
  \                                                                             \1 + \-1 + x / /              /
4(−9x2(4x2(x2−1)(x2−1)2+1−1)(x2−1)2+1+18x2(x2−1)2+1+2x(2x3+5)(8x2(x2−1)2(x2−1)2+1−5x2+3)((x2−1)2+1)2+3atan⁡(x2−1))4 \left(- \frac{9 x^{2} \left(\frac{4 x^{2} \left(x^{2} - 1\right)}{\left(x^{2} - 1\right)^{2} + 1} - 1\right)}{\left(x^{2} - 1\right)^{2} + 1} + \frac{18 x^{2}}{\left(x^{2} - 1\right)^{2} + 1} + \frac{2 x \left(2 x^{3} + 5\right) \left(\frac{8 x^{2} \left(x^{2} - 1\right)^{2}}{\left(x^{2} - 1\right)^{2} + 1} - 5 x^{2} + 3\right)}{\left(\left(x^{2} - 1\right)^{2} + 1\right)^{2}} + 3 \operatorname{atan}{\left(x^{2} - 1 \right)}\right)
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Gráfico
Derivada de y=(2x^3+5)arctan(x^2-1)
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