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y=arcsin5xtg(8x+3,14/4)

Derivada de y=arcsin5xtg(8x+3,14/4)

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Solución

Ha introducido [src]
             /      157 \
asin(5*x)*tan|8*x + ----|
             \      50*4/
$$\tan{\left(8 x + \frac{157}{4 \cdot 50} \right)} \operatorname{asin}{\left(5 x \right)}$$
asin(5*x)*tan(8*x + 157/(50*4))
Gráfica
Primera derivada [src]
                                          /      157 \
                                     5*tan|8*x + ----|
/         2/      157 \\                  \      50*4/
|8 + 8*tan |8*x + ----||*asin(5*x) + -----------------
\          \      50*4//                  ___________ 
                                         /         2  
                                       \/  1 - 25*x   
$$\left(8 \tan^{2}{\left(8 x + \frac{157}{4 \cdot 50} \right)} + 8\right) \operatorname{asin}{\left(5 x \right)} + \frac{5 \tan{\left(8 x + \frac{157}{4 \cdot 50} \right)}}{\sqrt{1 - 25 x^{2}}}$$
Segunda derivada [src]
   /       2/157      \\            /157      \                                                     
80*|1 + tan |--- + 8*x||   125*x*tan|--- + 8*x|                                                     
   \        \200      //            \200      /       /       2/157      \\              /157      \
------------------------ + -------------------- + 128*|1 + tan |--- + 8*x||*asin(5*x)*tan|--- + 8*x|
        ___________                      3/2          \        \200      //              \200      /
       /         2            /        2\                                                           
     \/  1 - 25*x             \1 - 25*x /                                                           
$$\frac{125 x \tan{\left(8 x + \frac{157}{200} \right)}}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}}} + 128 \left(\tan^{2}{\left(8 x + \frac{157}{200} \right)} + 1\right) \tan{\left(8 x + \frac{157}{200} \right)} \operatorname{asin}{\left(5 x \right)} + \frac{80 \left(\tan^{2}{\left(8 x + \frac{157}{200} \right)} + 1\right)}{\sqrt{1 - 25 x^{2}}}$$
Tercera derivada [src]
      /           2   \                                                                                                                                                         
      |       75*x    |    /157      \                                                                                                                                          
  125*|-1 + ----------|*tan|--- + 8*x|                                                                       /       2/157      \\    /157      \          /       2/157      \\
      |              2|    \200      /                                                                  1920*|1 + tan |--- + 8*x||*tan|--- + 8*x|   3000*x*|1 + tan |--- + 8*x||
      \     -1 + 25*x /                       /       2/157      \\ /         2/157      \\                  \        \200      //    \200      /          \        \200      //
- ------------------------------------ + 1024*|1 + tan |--- + 8*x||*|1 + 3*tan |--- + 8*x||*asin(5*x) + ----------------------------------------- + ----------------------------
                        3/2                   \        \200      // \          \200      //                              ___________                                  3/2       
             /        2\                                                                                                /         2                        /        2\          
             \1 - 25*x /                                                                                              \/  1 - 25*x                         \1 - 25*x /          
$$\frac{3000 x \left(\tan^{2}{\left(8 x + \frac{157}{200} \right)} + 1\right)}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}}} + 1024 \left(\tan^{2}{\left(8 x + \frac{157}{200} \right)} + 1\right) \left(3 \tan^{2}{\left(8 x + \frac{157}{200} \right)} + 1\right) \operatorname{asin}{\left(5 x \right)} + \frac{1920 \left(\tan^{2}{\left(8 x + \frac{157}{200} \right)} + 1\right) \tan{\left(8 x + \frac{157}{200} \right)}}{\sqrt{1 - 25 x^{2}}} - \frac{125 \left(\frac{75 x^{2}}{25 x^{2} - 1} - 1\right) \tan{\left(8 x + \frac{157}{200} \right)}}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}}}$$
Gráfico
Derivada de y=arcsin5xtg(8x+3,14/4)