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Сos3x×e^arctgx
Derivada de la función/ Сos3x/ arctg/ Сos3x×e^arctgx

Derivada de Сos3x×e^arctgx

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
          atan(x)
cos(3*x)*E
eatan⁡(x)cos⁡(3x)e^{\operatorname{atan}{\left(x \right)}} \cos{\left(3 x \right)} 
cos(3*x)*E^atan(x)
Gráfica
02468-8-6-4-2-1010-2525
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
                                  atan(x)
     atan(x)            cos(3*x)*e       
- 3*e       *sin(3*x) + -----------------
                                   2     
                              1 + x
−3eatan⁡(x)sin⁡(3x)+eatan⁡(x)cos⁡(3x)x2+1- 3 e^{\operatorname{atan}{\left(x \right)}} \sin{\left(3 x \right)} + \frac{e^{\operatorname{atan}{\left(x \right)}} \cos{\left(3 x \right)}}{x^{2} + 1}
Simplificar
Segunda derivada [src] 
 /             6*sin(3*x)   (-1 + 2*x)*cos(3*x)\  atan(x)
-|9*cos(3*x) + ---------- + -------------------|*e       
 |                    2                  2     |         
 |               1 + x           /     2\      |         
 \                               \1 + x /      /
−((2x−1)cos⁡(3x)(x2+1)2+9cos⁡(3x)+6sin⁡(3x)x2+1)eatan⁡(x)- \left(\frac{\left(2 x - 1\right) \cos{\left(3 x \right)}}{\left(x^{2} + 1\right)^{2}} + 9 \cos{\left(3 x \right)} + \frac{6 \sin{\left(3 x \right)}}{x^{2} + 1}\right) e^{\operatorname{atan}{\left(x \right)}}
Simplificar
Tercera derivada [src] 
/                            /                           2 \                                 \         
|                            |       1       6*x      8*x  |                                 |         
|                            |-2 + ------ - ------ + ------|*cos(3*x)                        |         
|                            |          2        2        2|                                 |         
|              27*cos(3*x)   \     1 + x    1 + x    1 + x /            9*(-1 + 2*x)*sin(3*x)|  atan(x)
|27*sin(3*x) - ----------- + ---------------------------------------- + ---------------------|*e       
|                      2                            2                                 2      |         
|                 1 + x                     /     2\                          /     2\       |         
\                                           \1 + x /                          \1 + x /       /
(9(2x−1)sin⁡(3x)(x2+1)2+27sin⁡(3x)−27cos⁡(3x)x2+1+(8x2x2+1−6xx2+1−2+1x2+1)cos⁡(3x)(x2+1)2)eatan⁡(x)\left(\frac{9 \left(2 x - 1\right) \sin{\left(3 x \right)}}{\left(x^{2} + 1\right)^{2}} + 27 \sin{\left(3 x \right)} - \frac{27 \cos{\left(3 x \right)}}{x^{2} + 1} + \frac{\left(\frac{8 x^{2}}{x^{2} + 1} - \frac{6 x}{x^{2} + 1} - 2 + \frac{1}{x^{2} + 1}\right) \cos{\left(3 x \right)}}{\left(x^{2} + 1\right)^{2}}\right) e^{\operatorname{atan}{\left(x \right)}}
Simplificar
Gráfico
Derivada de Сos3x×e^arctgx
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