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y=arccos²x×esinx
Derivada de la función/ cos²x/ arccos/ y=arccos²x×esinx

Derivada de y=arccos²x×esinx

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

Ha introducido [src] 
    2            
acos (x)*E*sin(x)
eacos⁡2(x)sin⁡(x)e \operatorname{acos}^{2}{\left(x \right)} \sin{\left(x \right)} 
(acos(x)^2*E)*sin(x)
Gráfica
02468-8-6-4-2-1010-5050
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
      2             2*E*acos(x)*sin(x)
E*acos (x)*cos(x) - ------------------
                          ________    
                         /      2     
                       \/  1 - x
ecos⁡(x)acos⁡2(x)−2esin⁡(x)acos⁡(x)1−x2e \cos{\left(x \right)} \operatorname{acos}^{2}{\left(x \right)} - \frac{2 e \sin{\left(x \right)} \operatorname{acos}{\left(x \right)}}{\sqrt{1 - x^{2}}}
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Segunda derivada [src] 
   /    2               /   1       x*acos(x) \          4*acos(x)*cos(x)\
-E*|acos (x)*sin(x) + 2*|------- + -----------|*sin(x) + ----------------|
   |                    |      2           3/2|               ________   |
   |                    |-1 + x    /     2\   |              /      2    |
   \                    \          \1 - x /   /            \/  1 - x     /
−e(2(xacos⁡(x)(1−x2)32+1x2−1)sin⁡(x)+sin⁡(x)acos⁡2(x)+4cos⁡(x)acos⁡(x)1−x2)- e \left(2 \left(\frac{x \operatorname{acos}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{1}{x^{2} - 1}\right) \sin{\left(x \right)} + \sin{\left(x \right)} \operatorname{acos}^{2}{\left(x \right)} + \frac{4 \cos{\left(x \right)} \operatorname{acos}{\left(x \right)}}{\sqrt{1 - x^{2}}}\right)
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Tercera derivada [src] 
  /                                                         /                              2        \                          \
  |      2               /   1       x*acos(x) \            |  acos(x)        3*x       3*x *acos(x)|          6*acos(x)*sin(x)|
E*|- acos (x)*cos(x) - 6*|------- + -----------|*cos(x) - 2*|----------- - ---------- + ------------|*sin(x) + ----------------|
  |                      |      2           3/2|            |        3/2            2           5/2 |               ________   |
  |                      |-1 + x    /     2\   |            |/     2\      /      2\    /     2\    |              /      2    |
  \                      \          \1 - x /   /            \\1 - x /      \-1 + x /    \1 - x /    /            \/  1 - x     /
e(−6(xacos⁡(x)(1−x2)32+1x2−1)cos⁡(x)−2(3x2acos⁡(x)(1−x2)52−3x(x2−1)2+acos⁡(x)(1−x2)32)sin⁡(x)−cos⁡(x)acos⁡2(x)+6sin⁡(x)acos⁡(x)1−x2)e \left(- 6 \left(\frac{x \operatorname{acos}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{1}{x^{2} - 1}\right) \cos{\left(x \right)} - 2 \left(\frac{3 x^{2} \operatorname{acos}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} - \frac{3 x}{\left(x^{2} - 1\right)^{2}} + \frac{\operatorname{acos}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}}\right) \sin{\left(x \right)} - \cos{\left(x \right)} \operatorname{acos}^{2}{\left(x \right)} + \frac{6 \sin{\left(x \right)} \operatorname{acos}{\left(x \right)}}{\sqrt{1 - x^{2}}}\right)
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Gráfico
Derivada de y=arccos²x×esinx
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