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y=8arcsin(1/(cbrt(x)))+(log(tg(x))/log(7))+3^(x^2)+(4x+8)^6
Derivada de la función/ y=8arcsin(1/(cbrt(x)))+(log(tg(x))/log(7))+3^(x^2)+(4x+8)^6

Derivada de y=8arcsin(1/(cbrt(x)))+(log(tg(x))/log(7))+3^(x^2)+(4x+8)^6

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

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Solución

Ha introducido [src] 
                               / 2\             
      /  1  \   log(tan(x))    \x /            6
8*asin|-----| + ----------- + 3     + (4*x + 8) 
      |3 ___|      log(7)                       
      \\/ x /
(3x2+(log⁡(tan⁡(x))log⁡(7)+8asin⁡(1x3)))+(4x+8)6\left(3^{x^{2}} + \left(\frac{\log{\left(\tan{\left(x \right)} \right)}}{\log{\left(7 \right)}} + 8 \operatorname{asin}{\left(\frac{1}{\sqrt[3]{x}} \right)}\right)\right) + \left(4 x + 8\right)^{6} 
8*asin(1/(x^(1/3))) + log(tan(x))/log(7) + 3^(x^2) + (4*x + 8)^6
Gráfica
02468-8-6-4-2-1010-3e493e49
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Primera derivada [src] 
                                                 2            / 2\       
            5             8               1 + tan (x)         \x /       
24*(4*x + 8)  - ---------------------- + ------------- + 2*x*3    *log(3)
                            __________   log(7)*tan(x)                   
                   4/3     /      1                                      
                3*x   *   /  1 - ----                                    
                         /        2/3                                    
                       \/        x
2⋅3x2xlog⁡(3)+24(4x+8)5+tan⁡2(x)+1log⁡(7)tan⁡(x)−83x431−1x232 \cdot 3^{x^{2}} x \log{\left(3 \right)} + 24 \left(4 x + 8\right)^{5} + \frac{\tan^{2}{\left(x \right)} + 1}{\log{\left(7 \right)} \tan{\left(x \right)}} - \frac{8}{3 x^{\frac{4}{3}} \sqrt{1 - \frac{1}{x^{\frac{2}{3}}}}}
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Segunda derivada [src] 
                                                                                                                2                     
                     / 2\            /       2   \                                                 /       2   \       / 2\           
              4      \x /          2*\1 + tan (x)/           8                      32             \1 + tan (x)/       \x /  2    2   
122880*(2 + x)  + 2*3    *log(3) + --------------- + ------------------ + ---------------------- - -------------- + 4*3    *x *log (3)
                                        log(7)                      3/2               __________             2                        
                                                        3 /     1  \         7/3     /      1      log(7)*tan (x)                     
                                                     9*x *|1 - ----|      9*x   *   /  1 - ----                                       
                                                          |     2/3|               /        2/3                                       
                                                          \    x   /             \/        x
4⋅3x2x2log⁡(3)2+2⋅3x2log⁡(3)+122880(x+2)4−(tan⁡2(x)+1)2log⁡(7)tan⁡2(x)+2(tan⁡2(x)+1)log⁡(7)+89x3(1−1x23)32+329x731−1x234 \cdot 3^{x^{2}} x^{2} \log{\left(3 \right)}^{2} + 2 \cdot 3^{x^{2}} \log{\left(3 \right)} + 122880 \left(x + 2\right)^{4} - \frac{\left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\log{\left(7 \right)} \tan^{2}{\left(x \right)}} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)}{\log{\left(7 \right)}} + \frac{8}{9 x^{3} \left(1 - \frac{1}{x^{\frac{2}{3}}}\right)^{\frac{3}{2}}} + \frac{32}{9 x^{\frac{7}{3}} \sqrt{1 - \frac{1}{x^{\frac{2}{3}}}}}
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Tercera derivada [src] 
  /                                                                                                        3                  2                                                                  \
  |                                                                                           /       2   \      /       2   \      /       2   \             / 2\                   / 2\        |
  |              3             112                       52                     4             \1 + tan (x)/    2*\1 + tan (x)/    2*\1 + tan (x)/*tan(x)      \x /  3    3           \x /    2   |
2*|245760*(2 + x)  - ------------------------ - ------------------- - --------------------- + -------------- - ---------------- + ---------------------- + 4*3    *x *log (3) + 6*x*3    *log (3)|
  |                                __________                   3/2                     5/2             3       log(7)*tan(x)             log(7)                                                 |
  |                      10/3     /      1          4 /     1  \         14/3 /     1  \      log(7)*tan (x)                                                                                     |
  |                  27*x    *   /  1 - ----    27*x *|1 - ----|      9*x    *|1 - ----|                                                                                                         |
  |                             /        2/3          |     2/3|              |     2/3|                                                                                                         |
  \                           \/        x             \    x   /              \    x   /                                                                                                         /
2(4⋅3x2x3log⁡(3)3+6⋅3x2xlog⁡(3)2+245760(x+2)3+(tan⁡2(x)+1)3log⁡(7)tan⁡3(x)−2(tan⁡2(x)+1)2log⁡(7)tan⁡(x)+2(tan⁡2(x)+1)tan⁡(x)log⁡(7)−5227x4(1−1x23)32−11227x1031−1x23−49x143(1−1x23)52)2 \left(4 \cdot 3^{x^{2}} x^{3} \log{\left(3 \right)}^{3} + 6 \cdot 3^{x^{2}} x \log{\left(3 \right)}^{2} + 245760 \left(x + 2\right)^{3} + \frac{\left(\tan^{2}{\left(x \right)} + 1\right)^{3}}{\log{\left(7 \right)} \tan^{3}{\left(x \right)}} - \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\log{\left(7 \right)} \tan{\left(x \right)}} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{\log{\left(7 \right)}} - \frac{52}{27 x^{4} \left(1 - \frac{1}{x^{\frac{2}{3}}}\right)^{\frac{3}{2}}} - \frac{112}{27 x^{\frac{10}{3}} \sqrt{1 - \frac{1}{x^{\frac{2}{3}}}}} - \frac{4}{9 x^{\frac{14}{3}} \left(1 - \frac{1}{x^{\frac{2}{3}}}\right)^{\frac{5}{2}}}\right)
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Gráfico
Derivada de y=8arcsin(1/(cbrt(x)))+(log(tg(x))/log(7))+3^(x^2)+(4x+8)^6
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