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y=asin^4(x*5^cosx)-lnx
Derivada de la función/ sin^4/ 5^cosx/ y=asin^4(x*5^cosx)-lnx

Derivada de y=asin^4(x*5^cosx)-lnx

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

Ha introducido [src] 
    4/   cos(x)\         
asin \x*5      / - log(x)
−log⁡(x)+asin⁡4(5cos⁡(x)x)- \log{\left(x \right)} + \operatorname{asin}^{4}{\left(5^{\cos{\left(x \right)}} x \right)} 
asin(x*5^cos(x))^4 - log(x)
Gráfica
02468-8-6-4-2-1010-200200
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
            3/   cos(x)\ / cos(x)      cos(x)              \
  1   4*asin \x*5      /*\5       - x*5      *log(5)*sin(x)/
- - + ------------------------------------------------------
  x                      __________________                 
                        /      2*cos(x)  2                  
                      \/  1 - 5        *x
4(−5cos⁡(x)xlog⁡(5)sin⁡(x)+5cos⁡(x))asin⁡3(5cos⁡(x)x)−52cos⁡(x)x2+1−1x\frac{4 \left(- 5^{\cos{\left(x \right)}} x \log{\left(5 \right)} \sin{\left(x \right)} + 5^{\cos{\left(x \right)}}\right) \operatorname{asin}^{3}{\left(5^{\cos{\left(x \right)}} x \right)}}{\sqrt{- 5^{2 \cos{\left(x \right)}} x^{2} + 1}} - \frac{1}{x}
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Segunda derivada [src] 
         2*cos(x)                       2     2/   cos(x)\      cos(x)     3/   cos(x)\ /                           2          \               3*cos(x)                       2     3/   cos(x)\
1    12*5        *(-1 + x*log(5)*sin(x)) *asin \x*5      /   4*5      *asin \x*5      /*\2*sin(x) + x*cos(x) - x*sin (x)*log(5)/*log(5)   4*x*5        *(-1 + x*log(5)*sin(x)) *asin \x*5      /
-- - ----------------------------------------------------- - -------------------------------------------------------------------------- + ------------------------------------------------------
 2                           2*cos(x)  2                                                  __________________                                                                3/2                 
x                      -1 + 5        *x                                                  /      2*cos(x)  2                                               /     2*cos(x)  2\                    
                                                                                       \/  1 - 5        *x                                                \1 - 5        *x /
4⋅53cos⁡(x)x(xlog⁡(5)sin⁡(x)−1)2asin⁡3(5cos⁡(x)x)(−52cos⁡(x)x2+1)32−12⋅52cos⁡(x)(xlog⁡(5)sin⁡(x)−1)2asin⁡2(5cos⁡(x)x)52cos⁡(x)x2−1−4⋅5cos⁡(x)(−xlog⁡(5)sin⁡2(x)+xcos⁡(x)+2sin⁡(x))log⁡(5)asin⁡3(5cos⁡(x)x)−52cos⁡(x)x2+1+1x2\frac{4 \cdot 5^{3 \cos{\left(x \right)}} x \left(x \log{\left(5 \right)} \sin{\left(x \right)} - 1\right)^{2} \operatorname{asin}^{3}{\left(5^{\cos{\left(x \right)}} x \right)}}{\left(- 5^{2 \cos{\left(x \right)}} x^{2} + 1\right)^{\frac{3}{2}}} - \frac{12 \cdot 5^{2 \cos{\left(x \right)}} \left(x \log{\left(5 \right)} \sin{\left(x \right)} - 1\right)^{2} \operatorname{asin}^{2}{\left(5^{\cos{\left(x \right)}} x \right)}}{5^{2 \cos{\left(x \right)}} x^{2} - 1} - \frac{4 \cdot 5^{\cos{\left(x \right)}} \left(- x \log{\left(5 \right)} \sin^{2}{\left(x \right)} + x \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right) \log{\left(5 \right)} \operatorname{asin}^{3}{\left(5^{\cos{\left(x \right)}} x \right)}}{\sqrt{- 5^{2 \cos{\left(x \right)}} x^{2} + 1}} + \frac{1}{x^{2}}
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Tercera derivada [src] 
  /           3*cos(x)                       3     /   cos(x)\         4*cos(x)                       3     2/   cos(x)\      5*cos(x)  2                       3     3/   cos(x)\      3*cos(x)     3/   cos(x)\                        /     2                                        2    2       2   \      cos(x)     3/   cos(x)\ /                            2                  2       3                              \              2*cos(x)     2/   cos(x)\                        /                           2          \               3*cos(x)     3/   cos(x)\                        /                           2          \       \
  |  1    12*5        *(-1 + x*log(5)*sin(x)) *asin\x*5      /   18*x*5        *(-1 + x*log(5)*sin(x)) *asin \x*5      /   6*5        *x *(-1 + x*log(5)*sin(x)) *asin \x*5      /   2*5        *asin \x*5      /*(-1 + x*log(5)*sin(x))*\1 - x *cos(x)*log(5) - 4*x*log(5)*sin(x) + 2*x *log (5)*sin (x)/   2*5      *asin \x*5      /*\-3*cos(x) + x*sin(x) + 3*sin (x)*log(5) - x*log (5)*sin (x) + 3*x*cos(x)*log(5)*sin(x)/*log(5)   18*5        *asin \x*5      /*(-1 + x*log(5)*sin(x))*\2*sin(x) + x*cos(x) - x*sin (x)*log(5)/*log(5)   4*x*5        *asin \x*5      /*(-1 + x*log(5)*sin(x))*\2*sin(x) + x*cos(x) - x*sin (x)*log(5)/*log(5)|
2*|- -- - ---------------------------------------------------- - ------------------------------------------------------- - ------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------- + -----------------------------------------------------------------------------------------------------|
  |   3                                    3/2                                                        2                                                       5/2                                                                                      3/2                                                                                                        __________________                                                                                                     2*cos(x)  2                                                                                                       3/2                                        |
  |  x                   /     2*cos(x)  2\                                        /      2*cos(x)  2\                                      /     2*cos(x)  2\                                                                       /     2*cos(x)  2\                                                                                                          /      2*cos(x)  2                                                                                                -1 + 5        *x                                                                                      /     2*cos(x)  2\                                           |
  \                      \1 - 5        *x /                                        \-1 + 5        *x /                                      \1 - 5        *x /                                                                       \1 - 5        *x /                                                                                                        \/  1 - 5        *x                                                                                                                                                                                                       \1 - 5        *x /                                           /
2(−6⋅55cos⁡(x)x2(xlog⁡(5)sin⁡(x)−1)3asin⁡3(5cos⁡(x)x)(−52cos⁡(x)x2+1)52−18⋅54cos⁡(x)x(xlog⁡(5)sin⁡(x)−1)3asin⁡2(5cos⁡(x)x)(52cos⁡(x)x2−1)2+4⋅53cos⁡(x)x(xlog⁡(5)sin⁡(x)−1)(−xlog⁡(5)sin⁡2(x)+xcos⁡(x)+2sin⁡(x))log⁡(5)asin⁡3(5cos⁡(x)x)(−52cos⁡(x)x2+1)32−12⋅53cos⁡(x)(xlog⁡(5)sin⁡(x)−1)3asin⁡(5cos⁡(x)x)(−52cos⁡(x)x2+1)32−2⋅53cos⁡(x)(xlog⁡(5)sin⁡(x)−1)(2x2log⁡(5)2sin⁡2(x)−x2log⁡(5)cos⁡(x)−4xlog⁡(5)sin⁡(x)+1)asin⁡3(5cos⁡(x)x)(−52cos⁡(x)x2+1)32−18⋅52cos⁡(x)(xlog⁡(5)sin⁡(x)−1)(−xlog⁡(5)sin⁡2(x)+xcos⁡(x)+2sin⁡(x))log⁡(5)asin⁡2(5cos⁡(x)x)52cos⁡(x)x2−1+2⋅5cos⁡(x)(−xlog⁡(5)2sin⁡3(x)+3xlog⁡(5)sin⁡(x)cos⁡(x)+xsin⁡(x)+3log⁡(5)sin⁡2(x)−3cos⁡(x))log⁡(5)asin⁡3(5cos⁡(x)x)−52cos⁡(x)x2+1−1x3)2 \left(- \frac{6 \cdot 5^{5 \cos{\left(x \right)}} x^{2} \left(x \log{\left(5 \right)} \sin{\left(x \right)} - 1\right)^{3} \operatorname{asin}^{3}{\left(5^{\cos{\left(x \right)}} x \right)}}{\left(- 5^{2 \cos{\left(x \right)}} x^{2} + 1\right)^{\frac{5}{2}}} - \frac{18 \cdot 5^{4 \cos{\left(x \right)}} x \left(x \log{\left(5 \right)} \sin{\left(x \right)} - 1\right)^{3} \operatorname{asin}^{2}{\left(5^{\cos{\left(x \right)}} x \right)}}{\left(5^{2 \cos{\left(x \right)}} x^{2} - 1\right)^{2}} + \frac{4 \cdot 5^{3 \cos{\left(x \right)}} x \left(x \log{\left(5 \right)} \sin{\left(x \right)} - 1\right) \left(- x \log{\left(5 \right)} \sin^{2}{\left(x \right)} + x \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right) \log{\left(5 \right)} \operatorname{asin}^{3}{\left(5^{\cos{\left(x \right)}} x \right)}}{\left(- 5^{2 \cos{\left(x \right)}} x^{2} + 1\right)^{\frac{3}{2}}} - \frac{12 \cdot 5^{3 \cos{\left(x \right)}} \left(x \log{\left(5 \right)} \sin{\left(x \right)} - 1\right)^{3} \operatorname{asin}{\left(5^{\cos{\left(x \right)}} x \right)}}{\left(- 5^{2 \cos{\left(x \right)}} x^{2} + 1\right)^{\frac{3}{2}}} - \frac{2 \cdot 5^{3 \cos{\left(x \right)}} \left(x \log{\left(5 \right)} \sin{\left(x \right)} - 1\right) \left(2 x^{2} \log{\left(5 \right)}^{2} \sin^{2}{\left(x \right)} - x^{2} \log{\left(5 \right)} \cos{\left(x \right)} - 4 x \log{\left(5 \right)} \sin{\left(x \right)} + 1\right) \operatorname{asin}^{3}{\left(5^{\cos{\left(x \right)}} x \right)}}{\left(- 5^{2 \cos{\left(x \right)}} x^{2} + 1\right)^{\frac{3}{2}}} - \frac{18 \cdot 5^{2 \cos{\left(x \right)}} \left(x \log{\left(5 \right)} \sin{\left(x \right)} - 1\right) \left(- x \log{\left(5 \right)} \sin^{2}{\left(x \right)} + x \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right) \log{\left(5 \right)} \operatorname{asin}^{2}{\left(5^{\cos{\left(x \right)}} x \right)}}{5^{2 \cos{\left(x \right)}} x^{2} - 1} + \frac{2 \cdot 5^{\cos{\left(x \right)}} \left(- x \log{\left(5 \right)}^{2} \sin^{3}{\left(x \right)} + 3 x \log{\left(5 \right)} \sin{\left(x \right)} \cos{\left(x \right)} + x \sin{\left(x \right)} + 3 \log{\left(5 \right)} \sin^{2}{\left(x \right)} - 3 \cos{\left(x \right)}\right) \log{\left(5 \right)} \operatorname{asin}^{3}{\left(5^{\cos{\left(x \right)}} x \right)}}{\sqrt{- 5^{2 \cos{\left(x \right)}} x^{2} + 1}} - \frac{1}{x^{3}}\right)
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Gráfico
Derivada de y=asin^4(x*5^cosx)-lnx
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