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y=ln(x)*sin(sqrt(x))-(ctg(x)/(cos(x)-1))+(arccos(x))^3-e^2
Derivada de la función/ y=ln(x)*sin(sqrt(x))-(ctg(x)/(cos(x)-1))+(arccos(x))^3-e^2

Derivada de y=ln(x)*sin(sqrt(x))-(ctg(x)/(cos(x)-1))+(arccos(x))^3-e^2

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

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Solución

Ha introducido [src] 
          /  ___\     cot(x)         3       2
log(x)*sin\\/ x / - ---------- + acos (x) - E 
                    cos(x) - 1
((log⁡(x)sin⁡(x)−cot⁡(x)cos⁡(x)−1)+acos⁡3(x))−e2\left(\left(\log{\left(x \right)} \sin{\left(\sqrt{x} \right)} - \frac{\cot{\left(x \right)}}{\cos{\left(x \right)} - 1}\right) + \operatorname{acos}^{3}{\left(x \right)}\right) - e^{2} 
log(x)*sin(sqrt(x)) - cot(x)/(cos(x) - 1) + acos(x)^3 - E^2
Gráfica
02468-8-6-4-2-1010-10000050000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
   /  ___\          2             2         /  ___\                       
sin\\/ x /   1 + cot (x)    3*acos (x)   cos\\/ x /*log(x)   cot(x)*sin(x)
---------- + ----------- - ----------- + ----------------- - -------------
    x         cos(x) - 1      ________            ___                    2
                             /      2         2*\/ x         (cos(x) - 1) 
                           \/  1 - x
cot⁡2(x)+1cos⁡(x)−1−sin⁡(x)cot⁡(x)(cos⁡(x)−1)2−3acos⁡2(x)1−x2+sin⁡(x)x+log⁡(x)cos⁡(x)2x\frac{\cot^{2}{\left(x \right)} + 1}{\cos{\left(x \right)} - 1} - \frac{\sin{\left(x \right)} \cot{\left(x \right)}}{\left(\cos{\left(x \right)} - 1\right)^{2}} - \frac{3 \operatorname{acos}^{2}{\left(x \right)}}{\sqrt{1 - x^{2}}} + \frac{\sin{\left(\sqrt{x} \right)}}{x} + \frac{\log{\left(x \right)} \cos{\left(\sqrt{x} \right)}}{2 \sqrt{x}}
Simplificar
Segunda derivada [src] 
   /  ___\      /  ___\                                        2        /       2   \               2               /       2   \                    /  ___\      /  ___\       
cos\\/ x /   sin\\/ x /   6*acos(x)   cos(x)*cot(x)    3*x*acos (x)   2*\1 + cot (x)/*cot(x)   2*sin (x)*cot(x)   2*\1 + cot (x)/*sin(x)   log(x)*sin\\/ x /   cos\\/ x /*log(x)
---------- - ---------- - --------- - -------------- - ------------ - ---------------------- - ---------------- + ---------------------- - ----------------- - -----------------
    3/2           2              2                 2           3/2         -1 + cos(x)                       3                     2              4*x                   3/2     
   x             x         -1 + x     (-1 + cos(x))    /     2\                                 (-1 + cos(x))         (-1 + cos(x))                                  4*x        
                                                       \1 - x /
−3xacos⁡2(x)(1−x2)32−2(cot⁡2(x)+1)cot⁡(x)cos⁡(x)−1+2(cot⁡2(x)+1)sin⁡(x)(cos⁡(x)−1)2−cos⁡(x)cot⁡(x)(cos⁡(x)−1)2−2sin⁡2(x)cot⁡(x)(cos⁡(x)−1)3−6acos⁡(x)x2−1−log⁡(x)sin⁡(x)4x−sin⁡(x)x2−log⁡(x)cos⁡(x)4x32+cos⁡(x)x32- \frac{3 x \operatorname{acos}^{2}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{2 \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)}}{\cos{\left(x \right)} - 1} + \frac{2 \left(\cot^{2}{\left(x \right)} + 1\right) \sin{\left(x \right)}}{\left(\cos{\left(x \right)} - 1\right)^{2}} - \frac{\cos{\left(x \right)} \cot{\left(x \right)}}{\left(\cos{\left(x \right)} - 1\right)^{2}} - \frac{2 \sin^{2}{\left(x \right)} \cot{\left(x \right)}}{\left(\cos{\left(x \right)} - 1\right)^{3}} - \frac{6 \operatorname{acos}{\left(x \right)}}{x^{2} - 1} - \frac{\log{\left(x \right)} \sin{\left(\sqrt{x} \right)}}{4 x} - \frac{\sin{\left(\sqrt{x} \right)}}{x^{2}} - \frac{\log{\left(x \right)} \cos{\left(\sqrt{x} \right)}}{4 x^{\frac{3}{2}}} + \frac{\cos{\left(\sqrt{x} \right)}}{x^{\frac{3}{2}}}
Simplificar
Tercera derivada [src] 
                                                            2                                                                                                                                                                                                                                                                                                       
                       2           /  ___\     /       2   \         /  ___\        /  ___\                       2     2           3               /       2   \               2    /       2   \        2    /       2   \                     /  ___\                      /  ___\        /  ___\                                     /       2   \              
       6         3*acos (x)   2*sin\\/ x /   2*\1 + cot (x)/    9*cos\\/ x /   3*sin\\/ x /   cot(x)*sin(x)    9*x *acos (x)   6*sin (x)*cot(x)   3*\1 + cot (x)/*cos(x)   4*cot (x)*\1 + cot (x)/   6*sin (x)*\1 + cot (x)/   18*x*acos(x)   cos\\/ x /*log(x)   3*log(x)*sin\\/ x /   3*cos\\/ x /*log(x)   6*cos(x)*cot(x)*sin(x)   6*\1 + cot (x)/*cot(x)*sin(x)
- ----------- - ----------- + ------------ + ---------------- - ------------ - ------------ + -------------- - ------------- - ---------------- + ---------------------- + ----------------------- + ----------------------- + ------------ - ----------------- + ------------------- + ------------------- - ---------------------- - -----------------------------
          3/2           3/2         3          -1 + cos(x)            5/2             2                    2            5/2                  4                     2             -1 + cos(x)                           3                 2             3/2                   2                    5/2                          3                            2       
  /     2\      /     2\           x                               4*x             4*x        (-1 + cos(x))     /     2\        (-1 + cos(x))         (-1 + cos(x))                                       (-1 + cos(x))         /      2\           8*x                   8*x                  8*x                (-1 + cos(x))                (-1 + cos(x))        
  \1 - x /      \1 - x /                                                                                        \1 - x /                                                                                                        \-1 + x /
−9x2acos⁡2(x)(1−x2)52+18xacos⁡(x)(x2−1)2+2(cot⁡2(x)+1)2cos⁡(x)−1+4(cot⁡2(x)+1)cot⁡2(x)cos⁡(x)−1−6(cot⁡2(x)+1)sin⁡(x)cot⁡(x)(cos⁡(x)−1)2+3(cot⁡2(x)+1)cos⁡(x)(cos⁡(x)−1)2+sin⁡(x)cot⁡(x)(cos⁡(x)−1)2+6(cot⁡2(x)+1)sin⁡2(x)(cos⁡(x)−1)3−6sin⁡(x)cos⁡(x)cot⁡(x)(cos⁡(x)−1)3−6sin⁡3(x)cot⁡(x)(cos⁡(x)−1)4−3acos⁡2(x)(1−x2)32−6(1−x2)32+3log⁡(x)sin⁡(x)8x2−3sin⁡(x)4x2+2sin⁡(x)x3−log⁡(x)cos⁡(x)8x32+3log⁡(x)cos⁡(x)8x52−9cos⁡(x)4x52- \frac{9 x^{2} \operatorname{acos}^{2}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{18 x \operatorname{acos}{\left(x \right)}}{\left(x^{2} - 1\right)^{2}} + \frac{2 \left(\cot^{2}{\left(x \right)} + 1\right)^{2}}{\cos{\left(x \right)} - 1} + \frac{4 \left(\cot^{2}{\left(x \right)} + 1\right) \cot^{2}{\left(x \right)}}{\cos{\left(x \right)} - 1} - \frac{6 \left(\cot^{2}{\left(x \right)} + 1\right) \sin{\left(x \right)} \cot{\left(x \right)}}{\left(\cos{\left(x \right)} - 1\right)^{2}} + \frac{3 \left(\cot^{2}{\left(x \right)} + 1\right) \cos{\left(x \right)}}{\left(\cos{\left(x \right)} - 1\right)^{2}} + \frac{\sin{\left(x \right)} \cot{\left(x \right)}}{\left(\cos{\left(x \right)} - 1\right)^{2}} + \frac{6 \left(\cot^{2}{\left(x \right)} + 1\right) \sin^{2}{\left(x \right)}}{\left(\cos{\left(x \right)} - 1\right)^{3}} - \frac{6 \sin{\left(x \right)} \cos{\left(x \right)} \cot{\left(x \right)}}{\left(\cos{\left(x \right)} - 1\right)^{3}} - \frac{6 \sin^{3}{\left(x \right)} \cot{\left(x \right)}}{\left(\cos{\left(x \right)} - 1\right)^{4}} - \frac{3 \operatorname{acos}^{2}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{6}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{3 \log{\left(x \right)} \sin{\left(\sqrt{x} \right)}}{8 x^{2}} - \frac{3 \sin{\left(\sqrt{x} \right)}}{4 x^{2}} + \frac{2 \sin{\left(\sqrt{x} \right)}}{x^{3}} - \frac{\log{\left(x \right)} \cos{\left(\sqrt{x} \right)}}{8 x^{\frac{3}{2}}} + \frac{3 \log{\left(x \right)} \cos{\left(\sqrt{x} \right)}}{8 x^{\frac{5}{2}}} - \frac{9 \cos{\left(\sqrt{x} \right)}}{4 x^{\frac{5}{2}}}
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Gráfico
Derivada de y=ln(x)*sin(sqrt(x))-(ctg(x)/(cos(x)-1))+(arccos(x))^3-e^2
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