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y=arcctg3x-7+6*tg(x)/(2)+4*e^(-x)

Derivada de y=arcctg3x-7+6*tg(x)/(2)+4*e^(-x)

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

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Solución

Ha introducido [src]
                6*tan(x)      -x
acot(3*x) - 7 + -------- + 4*E  
                   2            
$$\left(\left(\operatorname{acot}{\left(3 x \right)} - 7\right) + \frac{6 \tan{\left(x \right)}}{2}\right) + 4 e^{- x}$$
acot(3*x) - 7 + (6*tan(x))/2 + 4*E^(-x)
Gráfica
Primera derivada [src]
       -x      3            2   
3 - 4*e   - -------- + 3*tan (x)
                   2            
            1 + 9*x             
$$3 \tan^{2}{\left(x \right)} + 3 - 4 e^{- x} - \frac{3}{9 x^{2} + 1}$$
Segunda derivada [src]
  /   -x     /       2   \              27*x   \
2*|2*e   + 3*\1 + tan (x)/*tan(x) + -----------|
  |                                           2|
  |                                 /       2\ |
  \                                 \1 + 9*x / /
$$2 \left(\frac{27 x}{\left(9 x^{2} + 1\right)^{2}} + 3 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} + 2 e^{- x}\right)$$
Tercera derivada [src]
  /                         2                         2                            \
  |     -x     /       2   \         27          972*x           2    /       2   \|
2*|- 2*e   + 3*\1 + tan (x)/  + ----------- - ----------- + 6*tan (x)*\1 + tan (x)/|
  |                                       2             3                          |
  |                             /       2\    /       2\                           |
  \                             \1 + 9*x /    \1 + 9*x /                           /
$$2 \left(- \frac{972 x^{2}}{\left(9 x^{2} + 1\right)^{3}} + 3 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} + 6 \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{2}{\left(x \right)} - 2 e^{- x} + \frac{27}{\left(9 x^{2} + 1\right)^{2}}\right)$$
Gráfico
Derivada de y=arcctg3x-7+6*tg(x)/(2)+4*e^(-x)