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

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

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

Gráfico:

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Solución

Ha introducido [src] 
      ____                                                             
     /  5                                                              
   \/  x               x                                               
5*8        - log(x) + 9  + 12*cos(x) - 8*cot(x) + 3*acos(x) + 4*acot(x)
((((9x+(5⋅8x5−log⁡(x)))+12cos⁡(x))−8cot⁡(x))+3acos⁡(x))+4acot⁡(x)\left(\left(\left(\left(9^{x} + \left(5 \cdot 8^{\sqrt{x^{5}}} - \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*8^(sqrt(x^5)) - log(x) + 9^x + 12*cos(x) - 8*cot(x) + 3*acos(x) + 4*acot(x)
Gráfica
02468-8-6-4-2-1010-5e2885e288
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Primera derivada [src] 
                                                                          ____               
                                                                         /  5     ____       
                                                                       \/  x     /  5        
    1                 4           3             2       x          25*8       *\/  x  *log(8)
8 - - - 12*sin(x) - ------ - ----------- + 8*cot (x) + 9 *log(9) + --------------------------
    x                    2      ________                                      2*x            
                    1 + x      /      2                                                      
                             \/  1 - x
25⋅8x5x5log⁡(8)2x+9xlog⁡(9)−12sin⁡(x)+8cot⁡2(x)+8−4x2+1−31−x2−1x\frac{25 \cdot 8^{\sqrt{x^{5}}} \sqrt{x^{5}} \log{\left(8 \right)}}{2 x} + 9^{x} \log{\left(9 \right)} - 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] 
                                                                                          ____                     ____               
                                                                                         /  5                     /  5     ____       
                                                                                       \/  x    3    2          \/  x     /  5        
1                 x    2         /       2   \              3*x          8*x      125*8       *x *log (8)   75*8       *\/  x  *log(8)
-- - 12*cos(x) + 9 *log (9) - 16*\1 + cot (x)/*cot(x) - ----------- + --------- + ----------------------- + --------------------------
 2                                                              3/2           2              4                            2           
x                                                       /     2\      /     2\                                         4*x            
                                                        \1 - x /      \1 + x /
125⋅8x5x3log⁡(8)24+75⋅8x5x5log⁡(8)4x2+9xlog⁡(9)2+8x(x2+1)2−3x(1−x2)32−16(cot⁡2(x)+1)cot⁡(x)−12cos⁡(x)+1x2\frac{125 \cdot 8^{\sqrt{x^{5}}} x^{3} \log{\left(8 \right)}^{2}}{4} + \frac{75 \cdot 8^{\sqrt{x^{5}}} \sqrt{x^{5}} \log{\left(8 \right)}}{4 x^{2}} + 9^{x} \log{\left(9 \right)}^{2} + \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}}
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Tercera derivada [src] 
                                                                                                                                            ____                     ____                          ____                   
                                                                                                                                           /  5                     /  5     ____                 /  5        ____        
                                                             2                      2            2                                       \/  x    2    2          \/  x     /  5                \/  x    2   /  5     3   
       3        2        8                      /       2   \     x    3        32*x          9*x             2    /       2   \   1125*8       *x *log (8)   75*8       *\/  x  *log(8)   625*8       *x *\/  x  *log (8)
- ----------- - -- + --------- + 12*sin(x) + 16*\1 + cot (x)/  + 9 *log (9) - --------- - ----------- + 32*cot (x)*\1 + cot (x)/ + ------------------------ + -------------------------- + -------------------------------
          3/2    3           2                                                        3           5/2                                         8                             3                             8               
  /     2\      x    /     2\                                                 /     2\    /     2\                                                                       8*x                                              
  \1 - x /           \1 + x /                                                 \1 + x /    \1 - x /
625⋅8x5x2x5log⁡(8)38+1125⋅8x5x2log⁡(8)28+75⋅8x5x5log⁡(8)8x3+9xlog⁡(9)3−32x2(x2+1)3−9x2(1−x2)52+16(cot⁡2(x)+1)2+32(cot⁡2(x)+1)cot⁡2(x)+12sin⁡(x)+8(x2+1)2−3(1−x2)32−2x3\frac{625 \cdot 8^{\sqrt{x^{5}}} x^{2} \sqrt{x^{5}} \log{\left(8 \right)}^{3}}{8} + \frac{1125 \cdot 8^{\sqrt{x^{5}}} x^{2} \log{\left(8 \right)}^{2}}{8} + \frac{75 \cdot 8^{\sqrt{x^{5}}} \sqrt{x^{5}} \log{\left(8 \right)}}{8 x^{3}} + 9^{x} \log{\left(9 \right)}^{3} - \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}}
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Gráfico
Derivada de y=5(8^sqrt(x^5))-lnx+9^x+12cosx-8ctgx+3arccosx+4arctgx
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