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y=5^arcctg3x+x^4**sinx

Derivada de y=5^arcctg3x+x^4**sinx

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

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Solución

Ha introducido [src]
              / sin(x)\
 acot(3*x)    \4      /
5          + x         
$$5^{\operatorname{acot}{\left(3 x \right)}} + x^{4^{\sin{\left(x \right)}}}$$
5^acot(3*x) + x^(4^sin(x))
Gráfica
Primera derivada [src]
 / sin(x)\ / sin(x)                               \      acot(3*x)       
 \4      / |4          sin(x)                     |   3*5         *log(5)
x         *|------- + 4      *cos(x)*log(4)*log(x)| - -------------------
           \   x                                  /                2     
                                                            1 + 9*x      
$$- \frac{3 \cdot 5^{\operatorname{acot}{\left(3 x \right)}} \log{\left(5 \right)}}{9 x^{2} + 1} + x^{4^{\sin{\left(x \right)}}} \left(4^{\sin{\left(x \right)}} \log{\left(4 \right)} \log{\left(x \right)} \cos{\left(x \right)} + \frac{4^{\sin{\left(x \right)}}}{x}\right)$$
Segunda derivada [src]
           / sin(x)\                           2            / sin(x)\                                                                             acot(3*x)    2            acot(3*x)       
 2*sin(x)  \4      / /1                       \     sin(x)  \4      / /1                              2       2             2*cos(x)*log(4)\   9*5         *log (5)   54*x*5         *log(5)
4        *x         *|- + cos(x)*log(4)*log(x)|  - 4      *x         *|-- + log(4)*log(x)*sin(x) - cos (x)*log (4)*log(x) - ---------------| + -------------------- + ----------------------
                     \x                       /                       | 2                                                          x       |                 2                       2      
                                                                      \x                                                                   /       /       2\              /       2\       
                                                                                                                                                   \1 + 9*x /              \1 + 9*x /       
$$4^{2 \sin{\left(x \right)}} x^{4^{\sin{\left(x \right)}}} \left(\log{\left(4 \right)} \log{\left(x \right)} \cos{\left(x \right)} + \frac{1}{x}\right)^{2} - 4^{\sin{\left(x \right)}} x^{4^{\sin{\left(x \right)}}} \left(\log{\left(4 \right)} \log{\left(x \right)} \sin{\left(x \right)} - \log{\left(4 \right)}^{2} \log{\left(x \right)} \cos^{2}{\left(x \right)} - \frac{2 \log{\left(4 \right)} \cos{\left(x \right)}}{x} + \frac{1}{x^{2}}\right) + \frac{54 \cdot 5^{\operatorname{acot}{\left(3 x \right)}} x \log{\left(5 \right)}}{\left(9 x^{2} + 1\right)^{2}} + \frac{9 \cdot 5^{\operatorname{acot}{\left(3 x \right)}} \log{\left(5 \right)}^{2}}{\left(9 x^{2} + 1\right)^{2}}$$
Tercera derivada [src]
           / sin(x)\                           3            / sin(x)\ /                                                            2       2                                                                        \       acot(3*x)    3          acot(3*x)                acot(3*x)  2                 acot(3*x)    2                   / sin(x)\                                                                                                  
 3*sin(x)  \4      / /1                       \     sin(x)  \4      / |  2                              3       3             3*cos (x)*log (4)   3*log(4)*sin(x)   3*cos(x)*log(4)        2                        |   27*5         *log (5)   54*5         *log(5)   1944*5         *x *log(5)   486*x*5         *log (5)      2*sin(x)  \4      / /1                       \ /1                              2       2             2*cos(x)*log(4)\
4        *x         *|- + cos(x)*log(4)*log(x)|  - 4      *x         *|- -- + cos(x)*log(4)*log(x) - cos (x)*log (4)*log(x) - ----------------- + --------------- + --------------- + 3*log (4)*cos(x)*log(x)*sin(x)| - --------------------- + -------------------- - ------------------------- - ------------------------ - 3*4        *x         *|- + cos(x)*log(4)*log(x)|*|-- + log(4)*log(x)*sin(x) - cos (x)*log (4)*log(x) - ---------------|
                     \x                       /                       |   3                                                           x                  x                  2                                       |                  3                      2                         3                          3                                 \x                       / | 2                                                          x       |
                                                                      \  x                                                                                                 x                                        /        /       2\             /       2\                /       2\                 /       2\                                                             \x                                                                   /
                                                                                                                                                                                                                             \1 + 9*x /             \1 + 9*x /                \1 + 9*x /                 \1 + 9*x /                                                                                                                                   
$$4^{3 \sin{\left(x \right)}} x^{4^{\sin{\left(x \right)}}} \left(\log{\left(4 \right)} \log{\left(x \right)} \cos{\left(x \right)} + \frac{1}{x}\right)^{3} - 3 \cdot 4^{2 \sin{\left(x \right)}} x^{4^{\sin{\left(x \right)}}} \left(\log{\left(4 \right)} \log{\left(x \right)} \cos{\left(x \right)} + \frac{1}{x}\right) \left(\log{\left(4 \right)} \log{\left(x \right)} \sin{\left(x \right)} - \log{\left(4 \right)}^{2} \log{\left(x \right)} \cos^{2}{\left(x \right)} - \frac{2 \log{\left(4 \right)} \cos{\left(x \right)}}{x} + \frac{1}{x^{2}}\right) - 4^{\sin{\left(x \right)}} x^{4^{\sin{\left(x \right)}}} \left(3 \log{\left(4 \right)}^{2} \log{\left(x \right)} \sin{\left(x \right)} \cos{\left(x \right)} - \log{\left(4 \right)}^{3} \log{\left(x \right)} \cos^{3}{\left(x \right)} + \log{\left(4 \right)} \log{\left(x \right)} \cos{\left(x \right)} + \frac{3 \log{\left(4 \right)} \sin{\left(x \right)}}{x} - \frac{3 \log{\left(4 \right)}^{2} \cos^{2}{\left(x \right)}}{x} + \frac{3 \log{\left(4 \right)} \cos{\left(x \right)}}{x^{2}} - \frac{2}{x^{3}}\right) - \frac{1944 \cdot 5^{\operatorname{acot}{\left(3 x \right)}} x^{2} \log{\left(5 \right)}}{\left(9 x^{2} + 1\right)^{3}} - \frac{486 \cdot 5^{\operatorname{acot}{\left(3 x \right)}} x \log{\left(5 \right)}^{2}}{\left(9 x^{2} + 1\right)^{3}} + \frac{54 \cdot 5^{\operatorname{acot}{\left(3 x \right)}} \log{\left(5 \right)}}{\left(9 x^{2} + 1\right)^{2}} - \frac{27 \cdot 5^{\operatorname{acot}{\left(3 x \right)}} \log{\left(5 \right)}^{3}}{\left(9 x^{2} + 1\right)^{3}}$$
Gráfico
Derivada de y=5^arcctg3x+x^4**sinx