Sr Examen

Otras calculadoras

сos(3x-2)lnx+(4ctg(x^3))/(arcsinx)
Derivada de la función/ сos(3x-2)lnx+(4ctg(x^3))/(arcsinx)

Derivada de сos(3x-2)lnx+(4ctg(x^3))/(arcsinx)

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
                           / 3\
                      4*cot\x /
cos(3*x - 2)*log(x) + ---------
                       asin(x)
log⁡(x)cos⁡(3x−2)+4cot⁡(x3)asin⁡(x)\log{\left(x \right)} \cos{\left(3 x - 2 \right)} + \frac{4 \cot{\left(x^{3} \right)}}{\operatorname{asin}{\left(x \right)}} 
cos(3*x - 2)*log(x) + (4*cot(x^3))/asin(x)
Gráfica
02468-8-6-4-2-1010-20000002000000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
                                                 / 3\             2 /        2/ 3\\
cos(3*x - 2)                                4*cot\x /         12*x *\-1 - cot \x //
------------ - 3*log(x)*sin(3*x - 2) - -------------------- + ---------------------
     x                                    ________                   asin(x)       
                                         /      2      2                           
                                       \/  1 - x  *asin (x)
12x2(−cot⁡2(x3)−1)asin⁡(x)−3log⁡(x)sin⁡(3x−2)−4cot⁡(x3)1−x2asin⁡2(x)+cos⁡(3x−2)x\frac{12 x^{2} \left(- \cot^{2}{\left(x^{3} \right)} - 1\right)}{\operatorname{asin}{\left(x \right)}} - 3 \log{\left(x \right)} \sin{\left(3 x - 2 \right)} - \frac{4 \cot{\left(x^{3} \right)}}{\sqrt{1 - x^{2}} \operatorname{asin}^{2}{\left(x \right)}} + \frac{\cos{\left(3 x - 2 \right)}}{x}
Simplificar
Segunda derivada [src] 
                                                                  /       2/ 3\\            / 3\                   / 3\            2 /       2/ 3\\       4 /       2/ 3\\    / 3\
  cos(-2 + 3*x)                            6*sin(-2 + 3*x)   24*x*\1 + cot \x //       8*cot\x /            4*x*cot\x /        24*x *\1 + cot \x //   72*x *\1 + cot \x //*cot\x /
- ------------- - 9*cos(-2 + 3*x)*log(x) - --------------- - ------------------- - ------------------ - -------------------- + -------------------- + ----------------------------
         2                                        x                asin(x)         /      2\     3              3/2               ________                      asin(x)           
        x                                                                          \-1 + x /*asin (x)   /     2\        2        /      2      2                                  
                                                                                                        \1 - x /   *asin (x)   \/  1 - x  *asin (x)
72x4(cot⁡2(x3)+1)cot⁡(x3)asin⁡(x)+24x2(cot⁡2(x3)+1)1−x2asin⁡2(x)−24x(cot⁡2(x3)+1)asin⁡(x)−4xcot⁡(x3)(1−x2)32asin⁡2(x)−9log⁡(x)cos⁡(3x−2)−8cot⁡(x3)(x2−1)asin⁡3(x)−6sin⁡(3x−2)x−cos⁡(3x−2)x2\frac{72 x^{4} \left(\cot^{2}{\left(x^{3} \right)} + 1\right) \cot{\left(x^{3} \right)}}{\operatorname{asin}{\left(x \right)}} + \frac{24 x^{2} \left(\cot^{2}{\left(x^{3} \right)} + 1\right)}{\sqrt{1 - x^{2}} \operatorname{asin}^{2}{\left(x \right)}} - \frac{24 x \left(\cot^{2}{\left(x^{3} \right)} + 1\right)}{\operatorname{asin}{\left(x \right)}} - \frac{4 x \cot{\left(x^{3} \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{asin}^{2}{\left(x \right)}} - 9 \log{\left(x \right)} \cos{\left(3 x - 2 \right)} - \frac{8 \cot{\left(x^{3} \right)}}{\left(x^{2} - 1\right) \operatorname{asin}^{3}{\left(x \right)}} - \frac{6 \sin{\left(3 x - 2 \right)}}{x} - \frac{\cos{\left(3 x - 2 \right)}}{x^{2}}
Simplificar
Tercera derivada [src] 
                                                                                                                            2                                                                                                                                                                                                                                                                 
                        /       2/ 3\\                                                                      6 /       2/ 3\\               / 3\                  / 3\              6    2/ 3\ /       2/ 3\\          2    / 3\                   / 3\          3 /       2/ 3\\        /       2/ 3\\        2 /       2/ 3\\        3 /       2/ 3\\    / 3\        4 /       2/ 3\\    / 3\
  27*cos(-2 + 3*x)   24*\1 + cot \x //   2*cos(-2 + 3*x)   9*sin(-2 + 3*x)                             216*x *\1 + cot \x //         24*cot\x /             4*cot\x /         432*x *cot \x /*\1 + cot \x //      12*x *cot\x /           24*x*cot\x /      36*x *\1 + cot \x //   72*x*\1 + cot \x //    72*x *\1 + cot \x //   432*x *\1 + cot \x //*cot\x /   216*x *\1 + cot \x //*cot\x /
- ---------------- - ----------------- + --------------- + --------------- + 27*log(x)*sin(-2 + 3*x) - ---------------------- - -------------------- - -------------------- - ------------------------------ - -------------------- + ------------------- + -------------------- + -------------------- + -------------------- + ----------------------------- - -----------------------------
         x                asin(x)                3                 2                                          asin(x)                   3/2                    3/2                       asin(x)                       5/2                     2                    3/2               ________             /      2\     3                  asin(x)                      ________             
                                                x                 x                                                             /     2\        4      /     2\        2                                       /     2\        2      /      2\      3      /     2\        2        /      2      2       \-1 + x /*asin (x)                                           /      2      2       
                                                                                                                                \1 - x /   *asin (x)   \1 - x /   *asin (x)                                    \1 - x /   *asin (x)   \-1 + x / *asin (x)   \1 - x /   *asin (x)   \/  1 - x  *asin (x)                                                               \/  1 - x  *asin (x)
−216x6(cot⁡2(x3)+1)2asin⁡(x)−432x6(cot⁡2(x3)+1)cot⁡2(x3)asin⁡(x)−216x4(cot⁡2(x3)+1)cot⁡(x3)1−x2asin⁡2(x)+432x3(cot⁡2(x3)+1)cot⁡(x3)asin⁡(x)+36x3(cot⁡2(x3)+1)(1−x2)32asin⁡2(x)+72x2(cot⁡2(x3)+1)(x2−1)asin⁡3(x)−12x2cot⁡(x3)(1−x2)52asin⁡2(x)+24xcot⁡(x3)(x2−1)2asin⁡3(x)+72x(cot⁡2(x3)+1)1−x2asin⁡2(x)−24(cot⁡2(x3)+1)asin⁡(x)+27log⁡(x)sin⁡(3x−2)−4cot⁡(x3)(1−x2)32asin⁡2(x)−24cot⁡(x3)(1−x2)32asin⁡4(x)−27cos⁡(3x−2)x+9sin⁡(3x−2)x2+2cos⁡(3x−2)x3- \frac{216 x^{6} \left(\cot^{2}{\left(x^{3} \right)} + 1\right)^{2}}{\operatorname{asin}{\left(x \right)}} - \frac{432 x^{6} \left(\cot^{2}{\left(x^{3} \right)} + 1\right) \cot^{2}{\left(x^{3} \right)}}{\operatorname{asin}{\left(x \right)}} - \frac{216 x^{4} \left(\cot^{2}{\left(x^{3} \right)} + 1\right) \cot{\left(x^{3} \right)}}{\sqrt{1 - x^{2}} \operatorname{asin}^{2}{\left(x \right)}} + \frac{432 x^{3} \left(\cot^{2}{\left(x^{3} \right)} + 1\right) \cot{\left(x^{3} \right)}}{\operatorname{asin}{\left(x \right)}} + \frac{36 x^{3} \left(\cot^{2}{\left(x^{3} \right)} + 1\right)}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{asin}^{2}{\left(x \right)}} + \frac{72 x^{2} \left(\cot^{2}{\left(x^{3} \right)} + 1\right)}{\left(x^{2} - 1\right) \operatorname{asin}^{3}{\left(x \right)}} - \frac{12 x^{2} \cot{\left(x^{3} \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}} \operatorname{asin}^{2}{\left(x \right)}} + \frac{24 x \cot{\left(x^{3} \right)}}{\left(x^{2} - 1\right)^{2} \operatorname{asin}^{3}{\left(x \right)}} + \frac{72 x \left(\cot^{2}{\left(x^{3} \right)} + 1\right)}{\sqrt{1 - x^{2}} \operatorname{asin}^{2}{\left(x \right)}} - \frac{24 \left(\cot^{2}{\left(x^{3} \right)} + 1\right)}{\operatorname{asin}{\left(x \right)}} + 27 \log{\left(x \right)} \sin{\left(3 x - 2 \right)} - \frac{4 \cot{\left(x^{3} \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{asin}^{2}{\left(x \right)}} - \frac{24 \cot{\left(x^{3} \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{asin}^{4}{\left(x \right)}} - \frac{27 \cos{\left(3 x - 2 \right)}}{x} + \frac{9 \sin{\left(3 x - 2 \right)}}{x^{2}} + \frac{2 \cos{\left(3 x - 2 \right)}}{x^{3}}
Simplificar
Gráfico
Derivada de сos(3x-2)lnx+(4ctg(x^3))/(arcsinx)
    © Sr Examen – Калькулятор