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y=5(sqrt^8(x^5))-lnx+9^x+12cosx-8ctgx+3arccosx+4arctgx
Derivada de la función/ y=5(sqrt^8(x^5))-lnx+9^x+12cosx-8ctgx+3arccosx+4arctgx

Derivada de y=5(sqrt^8(x^5))-lnx+9^x+12cosx-8ctgx+3arccosx+4arctgx

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
         8                                                             
     ____                                                              
    /  5               x                                               
5*\/  x    - log(x) + 9  + 12*cos(x) - 8*cot(x) + 3*acos(x) + 4*acot(x)
$$\left(\left(\left(\left(9^{x} + \left(5 \left(\sqrt{x^{5}}\right)^{8} - \log{\left(x \right)}\right)\right) + 12 \cos{\left(x \right)}\right) - 8 \cot{\left(x \right)}\right) + 3 \operatorname{acos}{\left(x \right)}\right) + 4 \operatorname{acot}{\left(x \right)}$$ 
5*(sqrt(x^5))^8 - log(x) + 9^x + 12*cos(x) - 8*cot(x) + 3*acos(x) + 4*acot(x)
Gráfica
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Primera derivada [src] 
    1                 4           3             2           19    x       
8 - - - 12*sin(x) - ------ - ----------- + 8*cot (x) + 100*x   + 9 *log(9)
    x                    2      ________                                  
                    1 + x      /      2                                   
                             \/  1 - x
$$9^{x} \log{\left(9 \right)} + 100 x^{19} - 12 \sin{\left(x \right)} + 8 \cot^{2}{\left(x \right)} + 8 - \frac{4}{x^{2} + 1} - \frac{3}{\sqrt{1 - x^{2}}} - \frac{1}{x}$$
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Segunda derivada [src] 
1                      18    x    2         /       2   \              3*x          8*x   
-- - 12*cos(x) + 1900*x   + 9 *log (9) - 16*\1 + cot (x)/*cot(x) - ----------- + ---------
 2                                                                         3/2           2
x                                                                  /     2\      /     2\ 
                                                                   \1 - x /      \1 + x /
$$9^{x} \log{\left(9 \right)}^{2} + 1900 x^{18} + \frac{8 x}{\left(x^{2} + 1\right)^{2}} - \frac{3 x}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - 16 \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)} - 12 \cos{\left(x \right)} + \frac{1}{x^{2}}$$
Simplificar
Tercera derivada [src] 
                                                             2                                  2            2                              
       3        2        8                      /       2   \           17    x    3        32*x          9*x             2    /       2   \
- ----------- - -- + --------- + 12*sin(x) + 16*\1 + cot (x)/  + 34200*x   + 9 *log (9) - --------- - ----------- + 32*cot (x)*\1 + cot (x)/
          3/2    3           2                                                                    3           5/2                           
  /     2\      x    /     2\                                                             /     2\    /     2\                              
  \1 - x /           \1 + x /                                                             \1 + x /    \1 - x /
$$9^{x} \log{\left(9 \right)}^{3} + 34200 x^{17} - \frac{32 x^{2}}{\left(x^{2} + 1\right)^{3}} - \frac{9 x^{2}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + 16 \left(\cot^{2}{\left(x \right)} + 1\right)^{2} + 32 \left(\cot^{2}{\left(x \right)} + 1\right) \cot^{2}{\left(x \right)} + 12 \sin{\left(x \right)} + \frac{8}{\left(x^{2} + 1\right)^{2}} - \frac{3}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{2}{x^{3}}$$
Simplificar
Gráfico
Derivada de y=5(sqrt^8(x^5))-lnx+9^x+12cosx-8ctgx+3arccosx+4arctgx
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