Sr Examen

Otras calculadoras


(x+x^2)^(tan(2*x))

Derivada de (x+x^2)^(tan(2*x))

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
        tan(2*x)
/     2\        
\x + x /        
$$\left(x^{2} + x\right)^{\tan{\left(2 x \right)}}$$
(x + x^2)^tan(2*x)
Solución detallada
  1. No logro encontrar los pasos en la búsqueda de esta derivada.

    Perola derivada


Respuesta:

Gráfica
Primera derivada [src]
        tan(2*x)                                                     
/     2\         //         2     \    /     2\   (1 + 2*x)*tan(2*x)\
\x + x /        *|\2 + 2*tan (2*x)/*log\x + x / + ------------------|
                 |                                           2      |
                 \                                      x + x       /
$$\left(x^{2} + x\right)^{\tan{\left(2 x \right)}} \left(\frac{\left(2 x + 1\right) \tan{\left(2 x \right)}}{x^{2} + x} + \left(2 \tan^{2}{\left(2 x \right)} + 2\right) \log{\left(x^{2} + x \right)}\right)$$
Segunda derivada [src]
                    /                                                       2                                                                     2              /       2     \          \
           tan(2*x) |/  /       2     \                  (1 + 2*x)*tan(2*x)\    2*tan(2*x)     /       2     \                           (1 + 2*x) *tan(2*x)   4*\1 + tan (2*x)/*(1 + 2*x)|
(x*(1 + x))        *||2*\1 + tan (2*x)/*log(x*(1 + x)) + ------------------|  + ---------- + 8*\1 + tan (2*x)/*log(x*(1 + x))*tan(2*x) - ------------------- + ---------------------------|
                    |\                                       x*(1 + x)     /    x*(1 + x)                                                     2        2                x*(1 + x)         |
                    \                                                                                                                        x *(1 + x)                                   /
$$\left(x \left(x + 1\right)\right)^{\tan{\left(2 x \right)}} \left(\left(2 \left(\tan^{2}{\left(2 x \right)} + 1\right) \log{\left(x \left(x + 1\right) \right)} + \frac{\left(2 x + 1\right) \tan{\left(2 x \right)}}{x \left(x + 1\right)}\right)^{2} + 8 \left(\tan^{2}{\left(2 x \right)} + 1\right) \log{\left(x \left(x + 1\right) \right)} \tan{\left(2 x \right)} + \frac{4 \left(2 x + 1\right) \left(\tan^{2}{\left(2 x \right)} + 1\right)}{x \left(x + 1\right)} + \frac{2 \tan{\left(2 x \right)}}{x \left(x + 1\right)} - \frac{\left(2 x + 1\right)^{2} \tan{\left(2 x \right)}}{x^{2} \left(x + 1\right)^{2}}\right)$$
Tercera derivada [src]
                    /                                                       3                                                             /                                                                  2              /       2     \          \                     2                     /       2     \                                                            2 /       2     \                                     3               /       2     \                   \
           tan(2*x) |/  /       2     \                  (1 + 2*x)*tan(2*x)\      /  /       2     \                  (1 + 2*x)*tan(2*x)\ |2*tan(2*x)     /       2     \                           (1 + 2*x) *tan(2*x)   4*\1 + tan (2*x)/*(1 + 2*x)|      /       2     \                   12*\1 + tan (2*x)/         2      /       2     \                  6*(1 + 2*x) *\1 + tan (2*x)/   6*(1 + 2*x)*tan(2*x)   2*(1 + 2*x) *tan(2*x)   24*\1 + tan (2*x)/*(1 + 2*x)*tan(2*x)|
(x*(1 + x))        *||2*\1 + tan (2*x)/*log(x*(1 + x)) + ------------------|  + 3*|2*\1 + tan (2*x)/*log(x*(1 + x)) + ------------------|*|---------- + 8*\1 + tan (2*x)/*log(x*(1 + x))*tan(2*x) - ------------------- + ---------------------------| + 16*\1 + tan (2*x)/ *log(x*(1 + x)) + ------------------ + 32*tan (2*x)*\1 + tan (2*x)/*log(x*(1 + x)) - ---------------------------- - -------------------- + --------------------- + -------------------------------------|
                    |\                                       x*(1 + x)     /      \                                       x*(1 + x)     / |x*(1 + x)                                                     2        2                x*(1 + x)         |                                            x*(1 + x)                                                               2        2                 2        2              3        3                      x*(1 + x)              |
                    \                                                                                                                     \                                                             x *(1 + x)                                   /                                                                                                                   x *(1 + x)                 x *(1 + x)              x *(1 + x)                                              /
$$\left(x \left(x + 1\right)\right)^{\tan{\left(2 x \right)}} \left(\left(2 \left(\tan^{2}{\left(2 x \right)} + 1\right) \log{\left(x \left(x + 1\right) \right)} + \frac{\left(2 x + 1\right) \tan{\left(2 x \right)}}{x \left(x + 1\right)}\right)^{3} + 3 \left(2 \left(\tan^{2}{\left(2 x \right)} + 1\right) \log{\left(x \left(x + 1\right) \right)} + \frac{\left(2 x + 1\right) \tan{\left(2 x \right)}}{x \left(x + 1\right)}\right) \left(8 \left(\tan^{2}{\left(2 x \right)} + 1\right) \log{\left(x \left(x + 1\right) \right)} \tan{\left(2 x \right)} + \frac{4 \left(2 x + 1\right) \left(\tan^{2}{\left(2 x \right)} + 1\right)}{x \left(x + 1\right)} + \frac{2 \tan{\left(2 x \right)}}{x \left(x + 1\right)} - \frac{\left(2 x + 1\right)^{2} \tan{\left(2 x \right)}}{x^{2} \left(x + 1\right)^{2}}\right) + 16 \left(\tan^{2}{\left(2 x \right)} + 1\right)^{2} \log{\left(x \left(x + 1\right) \right)} + 32 \left(\tan^{2}{\left(2 x \right)} + 1\right) \log{\left(x \left(x + 1\right) \right)} \tan^{2}{\left(2 x \right)} + \frac{24 \left(2 x + 1\right) \left(\tan^{2}{\left(2 x \right)} + 1\right) \tan{\left(2 x \right)}}{x \left(x + 1\right)} + \frac{12 \left(\tan^{2}{\left(2 x \right)} + 1\right)}{x \left(x + 1\right)} - \frac{6 \left(2 x + 1\right)^{2} \left(\tan^{2}{\left(2 x \right)} + 1\right)}{x^{2} \left(x + 1\right)^{2}} - \frac{6 \left(2 x + 1\right) \tan{\left(2 x \right)}}{x^{2} \left(x + 1\right)^{2}} + \frac{2 \left(2 x + 1\right)^{3} \tan{\left(2 x \right)}}{x^{3} \left(x + 1\right)^{3}}\right)$$
Gráfico
Derivada de (x+x^2)^(tan(2*x))