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π/2-2*arccot(1/sqrt(lambertw(exp(1-(4*x)/1))))

Derivada de π/2-2*arccot(1/sqrt(lambertw(exp(1-(4*x)/1))))

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Gráfico:

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Solución

Ha introducido [src]
pi         /        1         \
-- - 2*acot|------------------|
2          |     _____________|
           |    /  /     4*x\ |
           |   /   | 1 - ---| |
           |  /    |      1 | |
           \\/    W\e       / /
$$- 2 \operatorname{acot}{\left(\frac{1}{\sqrt{W\left(e^{- \frac{4 x}{1} + 1}\right)}} \right)} + \frac{\pi}{2}$$
pi/2 - 2*acot(1/(sqrt(LambertW(exp(1 - 4*x/1)))))
Gráfica
Primera derivada [src]
                        4*x       4*x                 
                    1 - ---  -1 + ---                 
                         1         1                  
                 4*e       *e                         
------------------------------------------------------
                                         _____________
                  /     /     4*x\\     /  /     4*x\ 
                  |     | 1 - ---||    /   | 1 - ---| 
/         1     \ |     |      1 ||   /    |      1 | 
|1 + -----------|*\1 + W\e       //*\/    W\e       / 
|     /     4*x\|                                     
|     | 1 - ---||                                     
|     |      1 ||                                     
\    W\e       //                                     
$$\frac{4 e^{- \frac{4 x}{1} + 1} e^{\frac{4 x}{1} - 1}}{\left(1 + \frac{1}{W\left(e^{- \frac{4 x}{1} + 1}\right)}\right) \left(W\left(e^{- \frac{4 x}{1} + 1}\right) + 1\right) \sqrt{W\left(e^{- \frac{4 x}{1} + 1}\right)}}$$
Gráfico
Derivada de π/2-2*arccot(1/sqrt(lambertw(exp(1-(4*x)/1))))