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Derivada de la función/ y=ctg2e^x-(x*arccos3x)/(3-lnx)

Derivada de y=ctg2e^x-(x*arccos3x)/(3-lnx)

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

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Solución

Ha introducido [src] 
   x        x*acos(3*x)
cot (2*E) - -----------
             3 - log(x)
−xacos⁡(3x)3−log⁡(x)+cot⁡x(2e)- \frac{x \operatorname{acos}{\left(3 x \right)}}{3 - \log{\left(x \right)}} + \cot^{x}{\left(2 e \right)} 
cot(2*E)^x - x*acos(3*x)/(3 - log(x))
Primera derivada [src] 
                  3*x                                               
-acos(3*x) + -------------                                          
                __________                                          
               /        2                                           
             \/  1 - 9*x        x                        acos(3*x)  
-------------------------- + cot (2*E)*log(cot(2*E)) - -------------
        3 - log(x)                                                 2
                                                       (3 - log(x))
log⁡(cot⁡(2e))cot⁡x(2e)+3x1−9x2−acos⁡(3x)3−log⁡(x)−acos⁡(3x)(3−log⁡(x))2\log{\left(\cot{\left(2 e \right)} \right)} \cot^{x}{\left(2 e \right)} + \frac{\frac{3 x}{\sqrt{1 - 9 x^{2}}} - \operatorname{acos}{\left(3 x \right)}}{3 - \log{\left(x \right)}} - \frac{\operatorname{acos}{\left(3 x \right)}}{\left(3 - \log{\left(x \right)}\right)^{2}}
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Segunda derivada [src] 
                                                                            3*x                /         2  \                        
                                                          -acos(3*x) + -------------           |      9*x   |                        
                                                                          __________         3*|2 + --------|                        
                                                                         /        2            |           2|                        
   x         2                          3                              \/  1 - 9*x             \    1 - 9*x /          2*acos(3*x)   
cot (2*E)*log (cot(2*E)) + ---------------------------- + -------------------------- - --------------------------- + ----------------
                              __________                                      2           __________                                3
                             /        2               2        x*(-3 + log(x))           /        2                  x*(-3 + log(x)) 
                           \/  1 - 9*x  *(-3 + log(x))                                 \/  1 - 9*x  *(-3 + log(x))
log⁡(cot⁡(2e))2cot⁡x(2e)−3(9x21−9x2+2)1−9x2(log⁡(x)−3)+31−9x2(log⁡(x)−3)2+3x1−9x2−acos⁡(3x)x(log⁡(x)−3)2+2acos⁡(3x)x(log⁡(x)−3)3\log{\left(\cot{\left(2 e \right)} \right)}^{2} \cot^{x}{\left(2 e \right)} - \frac{3 \left(\frac{9 x^{2}}{1 - 9 x^{2}} + 2\right)}{\sqrt{1 - 9 x^{2}} \left(\log{\left(x \right)} - 3\right)} + \frac{3}{\sqrt{1 - 9 x^{2}} \left(\log{\left(x \right)} - 3\right)^{2}} + \frac{\frac{3 x}{\sqrt{1 - 9 x^{2}}} - \operatorname{acos}{\left(3 x \right)}}{x \left(\log{\left(x \right)} - 3\right)^{2}} + \frac{2 \operatorname{acos}{\left(3 x \right)}}{x \left(\log{\left(x \right)} - 3\right)^{3}}
Simplificar
Tercera derivada [src] 
                                             3*x                                                               /                  3*x     \                                                               /         2  \                /         2  \       
                           -acos(3*x) + -------------                                                        2*|-acos(3*x) + -------------|                                                               |     27*x   |                |      9*x   |       
                                           __________                                                          |                __________|                                                          27*x*|4 + --------|              6*|2 + --------|       
                                          /        2                                                           |               /        2 |                                                               |           2|                |           2|       
   x         3                          \/  1 - 9*x                   12                    6*acos(3*x)        \             \/  1 - 9*x  /      2*acos(3*x)                  27*x                        \    1 - 9*x /                \    1 - 9*x /       
cot (2*E)*log (cot(2*E)) - -------------------------- - ------------------------------ - ----------------- - ------------------------------ - ----------------- + ---------------------------- - --------------------------- + ------------------------------
                                2              2             __________                   2              4          2              3           2              3             3/2                            3/2                      __________               
                               x *(-3 + log(x))             /        2               3   x *(-3 + log(x))          x *(-3 + log(x))           x *(-3 + log(x))    /       2\                 2   /       2\                        /        2               2
                                                        x*\/  1 - 9*x  *(-3 + log(x))                                                                             \1 - 9*x /   *(-3 + log(x))    \1 - 9*x /   *(-3 + log(x))   x*\/  1 - 9*x  *(-3 + log(x))
−27x(27x21−9x2+4)(1−9x2)32(log⁡(x)−3)+27x(1−9x2)32(log⁡(x)−3)2+log⁡(cot⁡(2e))3cot⁡x(2e)+6(9x21−9x2+2)x1−9x2(log⁡(x)−3)2−12x1−9x2(log⁡(x)−3)3−3x1−9x2−acos⁡(3x)x2(log⁡(x)−3)2−2(3x1−9x2−acos⁡(3x))x2(log⁡(x)−3)3−2acos⁡(3x)x2(log⁡(x)−3)3−6acos⁡(3x)x2(log⁡(x)−3)4- \frac{27 x \left(\frac{27 x^{2}}{1 - 9 x^{2}} + 4\right)}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}} \left(\log{\left(x \right)} - 3\right)} + \frac{27 x}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}} \left(\log{\left(x \right)} - 3\right)^{2}} + \log{\left(\cot{\left(2 e \right)} \right)}^{3} \cot^{x}{\left(2 e \right)} + \frac{6 \left(\frac{9 x^{2}}{1 - 9 x^{2}} + 2\right)}{x \sqrt{1 - 9 x^{2}} \left(\log{\left(x \right)} - 3\right)^{2}} - \frac{12}{x \sqrt{1 - 9 x^{2}} \left(\log{\left(x \right)} - 3\right)^{3}} - \frac{\frac{3 x}{\sqrt{1 - 9 x^{2}}} - \operatorname{acos}{\left(3 x \right)}}{x^{2} \left(\log{\left(x \right)} - 3\right)^{2}} - \frac{2 \left(\frac{3 x}{\sqrt{1 - 9 x^{2}}} - \operatorname{acos}{\left(3 x \right)}\right)}{x^{2} \left(\log{\left(x \right)} - 3\right)^{3}} - \frac{2 \operatorname{acos}{\left(3 x \right)}}{x^{2} \left(\log{\left(x \right)} - 3\right)^{3}} - \frac{6 \operatorname{acos}{\left(3 x \right)}}{x^{2} \left(\log{\left(x \right)} - 3\right)^{4}}
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