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atan(x)*log(2*x+3)
Derivada de la función/ tan(x)/ 2*x+3/ atan(x)*log(2*x+3)

Derivada de atan(x)*log(2*x+3)

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

Ha introducido [src] 
atan(x)*log(2*x + 3)
log⁡(2x+3)atan⁡(x)\log{\left(2 x + 3 \right)} \operatorname{atan}{\left(x \right)} 
atan(x)*log(2*x + 3)
Gráfica
02468-8-6-4-2-1010-1010
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
log(2*x + 3)   2*atan(x)
------------ + ---------
        2       2*x + 3 
   1 + x
log⁡(2x+3)x2+1+2atan⁡(x)2x+3\frac{\log{\left(2 x + 3 \right)}}{x^{2} + 1} + \frac{2 \operatorname{atan}{\left(x \right)}}{2 x + 3}
Simplificar
Segunda derivada [src] 
  /  2*atan(x)            2            x*log(3 + 2*x)\
2*|- ---------- + ------------------ - --------------|
  |           2   /     2\                       2   |
  |  (3 + 2*x)    \1 + x /*(3 + 2*x)     /     2\    |
  \                                      \1 + x /    /
2(−xlog⁡(2x+3)(x2+1)2+2(2x+3)(x2+1)−2atan⁡(x)(2x+3)2)2 \left(- \frac{x \log{\left(2 x + 3 \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{2}{\left(2 x + 3\right) \left(x^{2} + 1\right)} - \frac{2 \operatorname{atan}{\left(x \right)}}{\left(2 x + 3\right)^{2}}\right)
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Tercera derivada [src] 
  /                                     /         2 \                                   \
  |                                     |      4*x  |                                   |
  |                                     |-1 + ------|*log(3 + 2*x)                      |
  |                                     |          2|                                   |
  |           6            8*atan(x)    \     1 + x /                        6*x        |
2*|- ------------------- + ---------- + -------------------------- - -------------------|
  |  /     2\          2            3                   2                    2          |
  |  \1 + x /*(3 + 2*x)    (3 + 2*x)            /     2\             /     2\           |
  \                                             \1 + x /             \1 + x / *(3 + 2*x)/
2(−6x(2x+3)(x2+1)2+(4x2x2+1−1)log⁡(2x+3)(x2+1)2−6(2x+3)2(x2+1)+8atan⁡(x)(2x+3)3)2 \left(- \frac{6 x}{\left(2 x + 3\right) \left(x^{2} + 1\right)^{2}} + \frac{\left(\frac{4 x^{2}}{x^{2} + 1} - 1\right) \log{\left(2 x + 3 \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{6}{\left(2 x + 3\right)^{2} \left(x^{2} + 1\right)} + \frac{8 \operatorname{atan}{\left(x \right)}}{\left(2 x + 3\right)^{3}}\right)
Simplificar
Gráfico
Derivada de atan(x)*log(2*x+3)
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