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y=sin^3arctg(e^(-√x))
Derivada de la función/ arctg/ sin^3/ y=sin/ y=sin^3arctg(e^(-√x))

Derivada de y=sin^3arctg(e^(-√x))

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

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Solución

Ha introducido [src] 
            /    ___\
   3        | -\/ x |
sin (x)*atan\E      /
sin⁡3(x)atan⁡(e−x)\sin^{3}{\left(x \right)} \operatorname{atan}{\left(e^{- \sqrt{x}} \right)} 
sin(x)^3*atan(E^(-sqrt(x)))
Gráfica
02468-8-6-4-2-10100.5-0.5
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Primera derivada [src] 
                                                 ___    
              /    ___\                 3     -\/ x     
     2        | -\/ x |              sin (x)*e          
3*sin (x)*atan\E      /*cos(x) - -----------------------
                                         /          ___\
                                     ___ |     -2*\/ x |
                                 2*\/ x *\1 + e        /
3sin⁡2(x)cos⁡(x)atan⁡(e−x)−e−xsin⁡3(x)2x(1+e−2x)3 \sin^{2}{\left(x \right)} \cos{\left(x \right)} \operatorname{atan}{\left(e^{- \sqrt{x}} \right)} - \frac{e^{- \sqrt{x}} \sin^{3}{\left(x \right)}}{2 \sqrt{x} \left(1 + e^{- 2 \sqrt{x}}\right)}
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Segunda derivada [src] 
/                                                  /                      ___   \                                  \       
|                                                  |                 -2*\/ x    |     ___                          |       
|                                             2    |1    1        2*e           |  -\/ x                           |       
|                                          sin (x)*|- + ---- - -----------------|*e                                |       
|                                                  |x    3/2     /          ___\|                        ___       |       
|                              /    ___\           |    x        |     -2*\/ x ||                     -\/ x        |       
|    /   2           2   \     | -\/ x |           \           x*\1 + e        //           3*cos(x)*e      *sin(x)|       
|- 3*\sin (x) - 2*cos (x)/*atan\E      / + ---------------------------------------------- - -----------------------|*sin(x)
|                                                          /          ___\                         /          ___\ |       
|                                                          |     -2*\/ x |                     ___ |     -2*\/ x | |       
\                                                        4*\1 + e        /                   \/ x *\1 + e        / /
(−3(sin⁡2(x)−2cos⁡2(x))atan⁡(e−x)+(1x−2e−2xx(1+e−2x)+1x32)e−xsin⁡2(x)4(1+e−2x)−3e−xsin⁡(x)cos⁡(x)x(1+e−2x))sin⁡(x)\left(- 3 \left(\sin^{2}{\left(x \right)} - 2 \cos^{2}{\left(x \right)}\right) \operatorname{atan}{\left(e^{- \sqrt{x}} \right)} + \frac{\left(\frac{1}{x} - \frac{2 e^{- 2 \sqrt{x}}}{x \left(1 + e^{- 2 \sqrt{x}}\right)} + \frac{1}{x^{\frac{3}{2}}}\right) e^{- \sqrt{x}} \sin^{2}{\left(x \right)}}{4 \left(1 + e^{- 2 \sqrt{x}}\right)} - \frac{3 e^{- \sqrt{x}} \sin{\left(x \right)} \cos{\left(x \right)}}{\sqrt{x} \left(1 + e^{- 2 \sqrt{x}}\right)}\right) \sin{\left(x \right)}
Simplificar
Tercera derivada [src] 
                                                             /                               ___                   ___                    ___     \                                                                                                           
                                                             |                          -2*\/ x               -2*\/ x                -4*\/ x      |     ___                                                      /                      ___   \               
                                                        3    | 1     3     3         8*e                   6*e                    8*e             |  -\/ x                                                       |                 -2*\/ x    |            ___
                                                     sin (x)*|---- + -- + ---- - -------------------- - ------------------ + ---------------------|*e                                                       2    |1    1        2*e           |         -\/ x 
                                                             | 3/2    2    5/2        /          ___\      /          ___\                       2|                                                    9*sin (x)*|- + ---- - -----------------|*cos(x)*e      
                                                             |x      x    x       3/2 |     -2*\/ x |    2 |     -2*\/ x |        /          ___\ |                                       ___                    |x    3/2     /          ___\|               
                                  /    ___\                  |                   x   *\1 + e        /   x *\1 + e        /    3/2 |     -2*\/ x | |             /   2           2   \  -\/ x                     |    x        |     -2*\/ x ||               
    /       2           2   \     | -\/ x |                  \                                                               x   *\1 + e        / /           9*\sin (x) - 2*cos (x)/*e      *sin(x)             \           x*\1 + e        //               
- 3*\- 2*cos (x) + 7*sin (x)/*atan\E      /*cos(x) - ------------------------------------------------------------------------------------------------------ + -------------------------------------- + -------------------------------------------------------
                                                                                                 /          ___\                                                             /          ___\                                /          ___\                   
                                                                                                 |     -2*\/ x |                                                         ___ |     -2*\/ x |                                |     -2*\/ x |                   
                                                                                               8*\1 + e        /                                                     2*\/ x *\1 + e        /                              4*\1 + e        /
−3(7sin⁡2(x)−2cos⁡2(x))cos⁡(x)atan⁡(e−x)+9(1x−2e−2xx(1+e−2x)+1x32)e−xsin⁡2(x)cos⁡(x)4(1+e−2x)−(3x2−6e−2xx2(1+e−2x)+1x32−8e−2xx32(1+e−2x)+8e−4xx32(1+e−2x)2+3x52)e−xsin⁡3(x)8(1+e−2x)+9(sin⁡2(x)−2cos⁡2(x))e−xsin⁡(x)2x(1+e−2x)- 3 \left(7 \sin^{2}{\left(x \right)} - 2 \cos^{2}{\left(x \right)}\right) \cos{\left(x \right)} \operatorname{atan}{\left(e^{- \sqrt{x}} \right)} + \frac{9 \left(\frac{1}{x} - \frac{2 e^{- 2 \sqrt{x}}}{x \left(1 + e^{- 2 \sqrt{x}}\right)} + \frac{1}{x^{\frac{3}{2}}}\right) e^{- \sqrt{x}} \sin^{2}{\left(x \right)} \cos{\left(x \right)}}{4 \left(1 + e^{- 2 \sqrt{x}}\right)} - \frac{\left(\frac{3}{x^{2}} - \frac{6 e^{- 2 \sqrt{x}}}{x^{2} \left(1 + e^{- 2 \sqrt{x}}\right)} + \frac{1}{x^{\frac{3}{2}}} - \frac{8 e^{- 2 \sqrt{x}}}{x^{\frac{3}{2}} \left(1 + e^{- 2 \sqrt{x}}\right)} + \frac{8 e^{- 4 \sqrt{x}}}{x^{\frac{3}{2}} \left(1 + e^{- 2 \sqrt{x}}\right)^{2}} + \frac{3}{x^{\frac{5}{2}}}\right) e^{- \sqrt{x}} \sin^{3}{\left(x \right)}}{8 \left(1 + e^{- 2 \sqrt{x}}\right)} + \frac{9 \left(\sin^{2}{\left(x \right)} - 2 \cos^{2}{\left(x \right)}\right) e^{- \sqrt{x}} \sin{\left(x \right)}}{2 \sqrt{x} \left(1 + e^{- 2 \sqrt{x}}\right)}
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Gráfico
Derivada de y=sin^3arctg(e^(-√x))
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