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y=arcctgx*log(x)/log(3)
Derivada de la función/ x*log/ log(x)/ log(3)/ y=arcctgx/ x*log(x)/log(3)/ y=arcctgx*log(x)/log(3)

Derivada de y=arcctgx*log(x)/log(3)

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Solución

Ha introducido [src] 
acot(x)*log(x)
--------------
    log(3)
log⁡(x)acot⁡(x)log⁡(3)\frac{\log{\left(x \right)} \operatorname{acot}{\left(x \right)}}{\log{\left(3 \right)}} 
(acot(x)*log(x))/log(3)
Gráfica
02468-8-6-4-2-1010-2020
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
acot(x)   log(x)
------- - ------
   x           2
          1 + x 
----------------
     log(3)
−log⁡(x)x2+1+acot⁡(x)xlog⁡(3)\frac{- \frac{\log{\left(x \right)}}{x^{2} + 1} + \frac{\operatorname{acot}{\left(x \right)}}{x}}{\log{\left(3 \right)}}
Simplificar
Segunda derivada [src] 
 /acot(x)       2        2*x*log(x)\ 
-|------- + ---------- - ----------| 
 |    2       /     2\           2 | 
 |   x      x*\1 + x /   /     2\  | 
 \                       \1 + x /  / 
-------------------------------------
                log(3)
−−2xlog⁡(x)(x2+1)2+2x(x2+1)+acot⁡(x)x2log⁡(3)- \frac{- \frac{2 x \log{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{2}{x \left(x^{2} + 1\right)} + \frac{\operatorname{acot}{\left(x \right)}}{x^{2}}}{\log{\left(3 \right)}}
Simplificar
Tercera derivada [src] 
                                        /         2 \       
                                        |      4*x  |       
                                      2*|-1 + ------|*log(x)
                                        |          2|       
    6       2*acot(x)        3          \     1 + x /       
--------- + --------- + ----------- - ----------------------
        2        3       2 /     2\                 2       
/     2\        x       x *\1 + x /         /     2\        
\1 + x /                                    \1 + x /        
------------------------------------------------------------
                           log(3)
−2(4x2x2+1−1)log⁡(x)(x2+1)2+6(x2+1)2+3x2(x2+1)+2acot⁡(x)x3log⁡(3)\frac{- \frac{2 \left(\frac{4 x^{2}}{x^{2} + 1} - 1\right) \log{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{6}{\left(x^{2} + 1\right)^{2}} + \frac{3}{x^{2} \left(x^{2} + 1\right)} + \frac{2 \operatorname{acot}{\left(x \right)}}{x^{3}}}{\log{\left(3 \right)}}
Simplificar
Gráfico
Derivada de y=arcctgx*log(x)/log(3)
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