Sr Examen

Otras calculadoras

y=x^arctg*x^2
Derivada de la función/ y=x^a/ arctg/ y=x^arctg*x^2

Derivada de y=x^arctg*x^2

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
     2   
 atan (x)
x
xatan⁡2(x)x^{\operatorname{atan}^{2}{\left(x \right)}} 
x^(atan(x)^2)
Solución detallada

  1. No logro encontrar los pasos en la búsqueda de esta derivada.

    Perola derivada

    (log⁡(atan⁡2(x))+1)∣atan⁡(x)∣2atan⁡2(x)\left(\log{\left(\operatorname{atan}^{2}{\left(x \right)} \right)} + 1\right) \left|{\operatorname{atan}{\left(x \right)}}\right|^{2 \operatorname{atan}^{2}{\left(x \right)}}

Respuesta:

(log⁡(atan⁡2(x))+1)∣atan⁡(x)∣2atan⁡2(x)\left(\log{\left(\operatorname{atan}^{2}{\left(x \right)} \right)} + 1\right) \left|{\operatorname{atan}{\left(x \right)}}\right|^{2 \operatorname{atan}^{2}{\left(x \right)}}

Gráfica
02468-8-6-4-2-1010-200200
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
     2    /    2                      \
 atan (x) |atan (x)   2*atan(x)*log(x)|
x        *|-------- + ----------------|
          |   x                 2     |
          \                1 + x      /
xatan⁡2(x)(2log⁡(x)atan⁡(x)x2+1+atan⁡2(x)x)x^{\operatorname{atan}^{2}{\left(x \right)}} \left(\frac{2 \log{\left(x \right)} \operatorname{atan}{\left(x \right)}}{x^{2} + 1} + \frac{\operatorname{atan}^{2}{\left(x \right)}}{x}\right)
Simplificar
Segunda derivada [src] 
     2    /                    2                2                                                 \
 atan (x) |/atan(x)   2*log(x)\      2      atan (x)    2*log(x)   4*atan(x)    4*x*atan(x)*log(x)|
x        *||------- + --------| *atan (x) - -------- + --------- + ---------- - ------------------|
          ||   x            2 |                 2              2     /     2\               2     |
          |\           1 + x  /                x       /     2\    x*\1 + x /       /     2\      |
          \                                            \1 + x /                     \1 + x /      /
xatan⁡2(x)(−4xlog⁡(x)atan⁡(x)(x2+1)2+(2log⁡(x)x2+1+atan⁡(x)x)2atan⁡2(x)+2log⁡(x)(x2+1)2+4atan⁡(x)x(x2+1)−atan⁡2(x)x2)x^{\operatorname{atan}^{2}{\left(x \right)}} \left(- \frac{4 x \log{\left(x \right)} \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \left(\frac{2 \log{\left(x \right)}}{x^{2} + 1} + \frac{\operatorname{atan}{\left(x \right)}}{x}\right)^{2} \operatorname{atan}^{2}{\left(x \right)} + \frac{2 \log{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{4 \operatorname{atan}{\left(x \right)}}{x \left(x^{2} + 1\right)} - \frac{\operatorname{atan}^{2}{\left(x \right)}}{x^{2}}\right)
Simplificar
Tercera derivada [src] 
     2    /                    3                               2                                                                                          /    2                                                 \               2               \
 atan (x) |/atan(x)   2*log(x)\      3      12*atan(x)   2*atan (x)        6        12*x*log(x)    6*atan(x)    4*atan(x)*log(x)     /atan(x)   2*log(x)\ |atan (x)    2*log(x)   4*atan(x)    4*x*atan(x)*log(x)|           16*x *atan(x)*log(x)|
x        *||------- + --------| *atan (x) - ---------- + ---------- + ----------- - ----------- - ----------- - ---------------- - 3*|------- + --------|*|-------- - --------- - ---------- + ------------------|*atan(x) + --------------------|
          ||   x            2 |                     2         3                 2            3     2 /     2\              2         |   x            2 | |    2              2     /     2\               2     |                        3      |
          |\           1 + x  /             /     2\         x          /     2\     /     2\     x *\1 + x /      /     2\          \           1 + x  / |   x       /     2\    x*\1 + x /       /     2\      |                /     2\       |
          \                                 \1 + x /                  x*\1 + x /     \1 + x /                      \1 + x /                               \           \1 + x /                     \1 + x /      /                \1 + x /       /
xatan⁡2(x)(16x2log⁡(x)atan⁡(x)(x2+1)3−12xlog⁡(x)(x2+1)3+(2log⁡(x)x2+1+atan⁡(x)x)3atan⁡3(x)−3(2log⁡(x)x2+1+atan⁡(x)x)(4xlog⁡(x)atan⁡(x)(x2+1)2−2log⁡(x)(x2+1)2−4atan⁡(x)x(x2+1)+atan⁡2(x)x2)atan⁡(x)−4log⁡(x)atan⁡(x)(x2+1)2−12atan⁡(x)(x2+1)2+6x(x2+1)2−6atan⁡(x)x2(x2+1)+2atan⁡2(x)x3)x^{\operatorname{atan}^{2}{\left(x \right)}} \left(\frac{16 x^{2} \log{\left(x \right)} \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{3}} - \frac{12 x \log{\left(x \right)}}{\left(x^{2} + 1\right)^{3}} + \left(\frac{2 \log{\left(x \right)}}{x^{2} + 1} + \frac{\operatorname{atan}{\left(x \right)}}{x}\right)^{3} \operatorname{atan}^{3}{\left(x \right)} - 3 \left(\frac{2 \log{\left(x \right)}}{x^{2} + 1} + \frac{\operatorname{atan}{\left(x \right)}}{x}\right) \left(\frac{4 x \log{\left(x \right)} \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{2 \log{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{4 \operatorname{atan}{\left(x \right)}}{x \left(x^{2} + 1\right)} + \frac{\operatorname{atan}^{2}{\left(x \right)}}{x^{2}}\right) \operatorname{atan}{\left(x \right)} - \frac{4 \log{\left(x \right)} \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{12 \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{6}{x \left(x^{2} + 1\right)^{2}} - \frac{6 \operatorname{atan}{\left(x \right)}}{x^{2} \left(x^{2} + 1\right)} + \frac{2 \operatorname{atan}^{2}{\left(x \right)}}{x^{3}}\right)
Simplificar
Gráfico
Derivada de y=x^arctg*x^2
    © Sr Examen – Калькулятор