Sr Examen

Otras calculadoras

y=5^arcctg3x+x^4*sinx
Derivada de la función/ x^4*sinx/ x+x^4/ ctg3x/ y=5^arcctg3x+x^4*sinx

Derivada de y=5^arcctg3x+x^4*sinx

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 acot(3*x)    4       
5          + x *sin(x)
5acot⁡(3x)+x4sin⁡(x)5^{\operatorname{acot}{\left(3 x \right)}} + x^{4} \sin{\left(x \right)} 
5^acot(3*x) + x^4*sin(x)
Gráfica
02468-8-6-4-2-1010-2000020000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
                             acot(3*x)       
 4             3          3*5         *log(5)
x *cos(x) + 4*x *sin(x) - -------------------
                                       2     
                                1 + 9*x
−3⋅5acot⁡(3x)log⁡(5)9x2+1+x4cos⁡(x)+4x3sin⁡(x)- \frac{3 \cdot 5^{\operatorname{acot}{\left(3 x \right)}} \log{\left(5 \right)}}{9 x^{2} + 1} + x^{4} \cos{\left(x \right)} + 4 x^{3} \sin{\left(x \right)}
Simplificar
Segunda derivada [src] 
                                              acot(3*x)    2            acot(3*x)       
   4             3              2          9*5         *log (5)   54*x*5         *log(5)
- x *sin(x) + 8*x *cos(x) + 12*x *sin(x) + -------------------- + ----------------------
                                                         2                       2      
                                               /       2\              /       2\       
                                               \1 + 9*x /              \1 + 9*x /
54⋅5acot⁡(3x)xlog⁡(5)(9x2+1)2+9⋅5acot⁡(3x)log⁡(5)2(9x2+1)2−x4sin⁡(x)+8x3cos⁡(x)+12x2sin⁡(x)\frac{54 \cdot 5^{\operatorname{acot}{\left(3 x \right)}} x \log{\left(5 \right)}}{\left(9 x^{2} + 1\right)^{2}} + \frac{9 \cdot 5^{\operatorname{acot}{\left(3 x \right)}} \log{\left(5 \right)}^{2}}{\left(9 x^{2} + 1\right)^{2}} - x^{4} \sin{\left(x \right)} + 8 x^{3} \cos{\left(x \right)} + 12 x^{2} \sin{\left(x \right)}
Simplificar
Tercera derivada [src] 
                                                              acot(3*x)    3          acot(3*x)                acot(3*x)  2                 acot(3*x)    2   
   4              3                            2          27*5         *log (5)   54*5         *log(5)   1944*5         *x *log(5)   486*x*5         *log (5)
- x *cos(x) - 12*x *sin(x) + 24*x*sin(x) + 36*x *cos(x) - --------------------- + -------------------- - ------------------------- - ------------------------
                                                                         3                      2                         3                          3       
                                                               /       2\             /       2\                /       2\                 /       2\        
                                                               \1 + 9*x /             \1 + 9*x /                \1 + 9*x /                 \1 + 9*x /
−1944⋅5acot⁡(3x)x2log⁡(5)(9x2+1)3−486⋅5acot⁡(3x)xlog⁡(5)2(9x2+1)3+54⋅5acot⁡(3x)log⁡(5)(9x2+1)2−27⋅5acot⁡(3x)log⁡(5)3(9x2+1)3−x4cos⁡(x)−12x3sin⁡(x)+36x2cos⁡(x)+24xsin⁡(x)- \frac{1944 \cdot 5^{\operatorname{acot}{\left(3 x \right)}} x^{2} \log{\left(5 \right)}}{\left(9 x^{2} + 1\right)^{3}} - \frac{486 \cdot 5^{\operatorname{acot}{\left(3 x \right)}} x \log{\left(5 \right)}^{2}}{\left(9 x^{2} + 1\right)^{3}} + \frac{54 \cdot 5^{\operatorname{acot}{\left(3 x \right)}} \log{\left(5 \right)}}{\left(9 x^{2} + 1\right)^{2}} - \frac{27 \cdot 5^{\operatorname{acot}{\left(3 x \right)}} \log{\left(5 \right)}^{3}}{\left(9 x^{2} + 1\right)^{3}} - x^{4} \cos{\left(x \right)} - 12 x^{3} \sin{\left(x \right)} + 36 x^{2} \cos{\left(x \right)} + 24 x \sin{\left(x \right)}
Simplificar
Gráfico
Derivada de y=5^arcctg3x+x^4*sinx
    © Sr Examen – Калькулятор