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y=e^x*sinx+sqrt(5-4x)-tgx/arccosx
Derivada de la función/ y=e^x*sinx+sqrt(5-4x)-tgx/arccosx

Derivada de y=e^x*sinx+sqrt(5-4x)-tgx/arccosx

Función f() - derivada -er orden en el punto
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Gráfico:

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Solución

Ha introducido [src] 
 x            _________    tan(x)
E *sin(x) + \/ 5 - 4*x  - -------
                          acos(x)
(exsin⁡(x)+5−4x)−tan⁡(x)acos⁡(x)\left(e^{x} \sin{\left(x \right)} + \sqrt{5 - 4 x}\right) - \frac{\tan{\left(x \right)}}{\operatorname{acos}{\left(x \right)}} 
E^x*sin(x) + sqrt(5 - 4*x) - tan(x)/acos(x)
Gráfica
02468-8-6-4-2-1010-2525
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
                        2                                                  
       2        -1 - tan (x)           x    x                 tan(x)       
- ----------- + ------------ + cos(x)*e  + e *sin(x) - --------------------
    _________     acos(x)                                 ________         
  \/ 5 - 4*x                                             /      2      2   
                                                       \/  1 - x  *acos (x)
−tan⁡2(x)−1acos⁡(x)+exsin⁡(x)+excos⁡(x)−25−4x−tan⁡(x)1−x2acos⁡2(x)\frac{- \tan^{2}{\left(x \right)} - 1}{\operatorname{acos}{\left(x \right)}} + e^{x} \sin{\left(x \right)} + e^{x} \cos{\left(x \right)} - \frac{2}{\sqrt{5 - 4 x}} - \frac{\tan{\left(x \right)}}{\sqrt{1 - x^{2}} \operatorname{acos}^{2}{\left(x \right)}}
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Segunda derivada [src] 
                                   /       2   \        /       2   \                                                   
       4                   x     2*\1 + tan (x)/      2*\1 + tan (x)/*tan(x)        2*tan(x)              x*tan(x)      
- ------------ + 2*cos(x)*e  - -------------------- - ---------------------- + ------------------ - --------------------
           3/2                    ________                   acos(x)           /      2\     3              3/2         
  (5 - 4*x)                      /      2      2                               \-1 + x /*acos (x)   /     2\        2   
                               \/  1 - x  *acos (x)                                                 \1 - x /   *acos (x)
−xtan⁡(x)(1−x2)32acos⁡2(x)−2(tan⁡2(x)+1)tan⁡(x)acos⁡(x)+2excos⁡(x)+2tan⁡(x)(x2−1)acos⁡3(x)−4(5−4x)32−2(tan⁡2(x)+1)1−x2acos⁡2(x)- \frac{x \tan{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{acos}^{2}{\left(x \right)}} - \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{\operatorname{acos}{\left(x \right)}} + 2 e^{x} \cos{\left(x \right)} + \frac{2 \tan{\left(x \right)}}{\left(x^{2} - 1\right) \operatorname{acos}^{3}{\left(x \right)}} - \frac{4}{\left(5 - 4 x\right)^{\frac{3}{2}}} - \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)}{\sqrt{1 - x^{2}} \operatorname{acos}^{2}{\left(x \right)}}
Simplificar
Tercera derivada [src] 
                                2                                                                                                                                                                                                                      
                   /       2   \                                                                                   2    /       2   \      /       2   \                             /       2   \               /       2   \            2            
       24        2*\1 + tan (x)/       x                    x          tan(x)                6*tan(x)         4*tan (x)*\1 + tan (x)/    6*\1 + tan (x)/          6*x*tan(x)       6*\1 + tan (x)/*tan(x)    3*x*\1 + tan (x)/         3*x *tan(x)     
- ------------ - ---------------- - 2*e *sin(x) + 2*cos(x)*e  - -------------------- - -------------------- - ----------------------- + ------------------ - ------------------- - ---------------------- - -------------------- - --------------------
           5/2       acos(x)                                            3/2                    3/2                    acos(x)           /      2\     3               2                ________                     3/2                    5/2         
  (5 - 4*x)                                                     /     2\        2      /     2\        4                                \-1 + x /*acos (x)   /      2\      3         /      2      2       /     2\        2      /     2\        2   
                                                                \1 - x /   *acos (x)   \1 - x /   *acos (x)                                                  \-1 + x / *acos (x)    \/  1 - x  *acos (x)    \1 - x /   *acos (x)   \1 - x /   *acos (x)
−3x2tan⁡(x)(1−x2)52acos⁡2(x)−6xtan⁡(x)(x2−1)2acos⁡3(x)−3x(tan⁡2(x)+1)(1−x2)32acos⁡2(x)−2(tan⁡2(x)+1)2acos⁡(x)−4(tan⁡2(x)+1)tan⁡2(x)acos⁡(x)−2exsin⁡(x)+2excos⁡(x)+6(tan⁡2(x)+1)(x2−1)acos⁡3(x)−24(5−4x)52−6(tan⁡2(x)+1)tan⁡(x)1−x2acos⁡2(x)−tan⁡(x)(1−x2)32acos⁡2(x)−6tan⁡(x)(1−x2)32acos⁡4(x)- \frac{3 x^{2} \tan{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}} \operatorname{acos}^{2}{\left(x \right)}} - \frac{6 x \tan{\left(x \right)}}{\left(x^{2} - 1\right)^{2} \operatorname{acos}^{3}{\left(x \right)}} - \frac{3 x \left(\tan^{2}{\left(x \right)} + 1\right)}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{acos}^{2}{\left(x \right)}} - \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\operatorname{acos}{\left(x \right)}} - \frac{4 \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{2}{\left(x \right)}}{\operatorname{acos}{\left(x \right)}} - 2 e^{x} \sin{\left(x \right)} + 2 e^{x} \cos{\left(x \right)} + \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right)}{\left(x^{2} - 1\right) \operatorname{acos}^{3}{\left(x \right)}} - \frac{24}{\left(5 - 4 x\right)^{\frac{5}{2}}} - \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{\sqrt{1 - x^{2}} \operatorname{acos}^{2}{\left(x \right)}} - \frac{\tan{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{acos}^{2}{\left(x \right)}} - \frac{6 \tan{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{acos}^{4}{\left(x \right)}}
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Gráfico
Derivada de y=e^x*sinx+sqrt(5-4x)-tgx/arccosx
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