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y=arccoslnsinx
Derivada de la función/ arccos/ lnsinx/ y=arccoslnsinx

Derivada de y=arccoslnsinx

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

Ha introducido [src] 
acos(x)*log(sin(x))
log⁡(sin⁡(x))acos⁡(x)\log{\left(\sin{\left(x \right)} \right)} \operatorname{acos}{\left(x \right)} 
acos(x)*log(sin(x))
Gráfica
02468-8-6-4-2-1010-2020
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Trazar el gráfico f'(x)
Primera derivada [src] 
  log(sin(x))   acos(x)*cos(x)
- ----------- + --------------
     ________       sin(x)    
    /      2                  
  \/  1 - x
cos⁡(x)acos⁡(x)sin⁡(x)−log⁡(sin⁡(x))1−x2\frac{\cos{\left(x \right)} \operatorname{acos}{\left(x \right)}}{\sin{\left(x \right)}} - \frac{\log{\left(\sin{\left(x \right)} \right)}}{\sqrt{1 - x^{2}}}
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Segunda derivada [src] 
 //       2   \                                             \
 ||    cos (x)|           x*log(sin(x))        2*cos(x)     |
-||1 + -------|*acos(x) + ------------- + ------------------|
 ||       2   |                    3/2       ________       |
 |\    sin (x)/            /     2\         /      2        |
 \                         \1 - x /       \/  1 - x  *sin(x)/
−(xlog⁡(sin⁡(x))(1−x2)32+(1+cos⁡2(x)sin⁡2(x))acos⁡(x)+2cos⁡(x)1−x2sin⁡(x))- (\frac{x \log{\left(\sin{\left(x \right)} \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \left(1 + \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \operatorname{acos}{\left(x \right)} + \frac{2 \cos{\left(x \right)}}{\sqrt{1 - x^{2}} \sin{\left(x \right)}})
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Tercera derivada [src] 
  /       2   \   /          2 \                                      /       2   \               
  |    cos (x)|   |       3*x  |                                      |    cos (x)|               
3*|1 + -------|   |-1 + -------|*log(sin(x))                        2*|1 + -------|*acos(x)*cos(x)
  |       2   |   |           2|                                      |       2   |               
  \    sin (x)/   \     -1 + x /                   3*x*cos(x)         \    sin (x)/               
--------------- + -------------------------- - ------------------ + ------------------------------
     ________                    3/2                   3/2                      sin(x)            
    /      2             /     2\              /     2\                                           
  \/  1 - x              \1 - x /              \1 - x /   *sin(x)
−3xcos⁡(x)(1−x2)32sin⁡(x)+2(1+cos⁡2(x)sin⁡2(x))cos⁡(x)acos⁡(x)sin⁡(x)+3(1+cos⁡2(x)sin⁡2(x))1−x2+(3x2x2−1−1)log⁡(sin⁡(x))(1−x2)32- \frac{3 x \cos{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \sin{\left(x \right)}} + \frac{2 \left(1 + \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \cos{\left(x \right)} \operatorname{acos}{\left(x \right)}}{\sin{\left(x \right)}} + \frac{3 \left(1 + \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right)}{\sqrt{1 - x^{2}}} + \frac{\left(\frac{3 x^{2}}{x^{2} - 1} - 1\right) \log{\left(\sin{\left(x \right)} \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}}
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Gráfico
Derivada de y=arccoslnsinx
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