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y=7^x/arctgx
Derivada de la función/ y=7^x/ arctg/ y=7^x/arctgx

Derivada de y=7^x/arctgx

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

Ha introducido [src] 
    x  
   7   
-------
acot(x)
7xacot⁡(x)\frac{7^{x}}{\operatorname{acot}{\left(x \right)}} 
7^x/acot(x)
Gráfica
02468-8-6-4-2-1010-500000000010000000000
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Primera derivada [src] 
         x           x       
        7           7 *log(7)
----------------- + ---------
/     2\     2       acot(x) 
\1 + x /*acot (x)
7xlog⁡(7)acot⁡(x)+7x(x2+1)acot⁡2(x)\frac{7^{x} \log{\left(7 \right)}}{\operatorname{acot}{\left(x \right)}} + \frac{7^{x}}{\left(x^{2} + 1\right) \operatorname{acot}^{2}{\left(x \right)}}
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Segunda derivada [src] 
   /             /       1   \                    \
   |           2*|x - -------|                    |
 x |   2         \    acot(x)/        2*log(7)    |
7 *|log (7) - ----------------- + ----------------|
   |                  2           /     2\        |
   |          /     2\            \1 + x /*acot(x)|
   \          \1 + x / *acot(x)                   /
---------------------------------------------------
                      acot(x)
7x(−2(x−1acot⁡(x))(x2+1)2acot⁡(x)+log⁡(7)2+2log⁡(7)(x2+1)acot⁡(x))acot⁡(x)\frac{7^{x} \left(- \frac{2 \left(x - \frac{1}{\operatorname{acot}{\left(x \right)}}\right)}{\left(x^{2} + 1\right)^{2} \operatorname{acot}{\left(x \right)}} + \log{\left(7 \right)}^{2} + \frac{2 \log{\left(7 \right)}}{\left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}}\right)}{\operatorname{acot}{\left(x \right)}}
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Tercera derivada [src] 
   /            /                             2                    \                                            \
   |            |             3            4*x           6*x       |                                            |
   |          2*|-1 + ----------------- + ------ - ----------------|                        /       1   \       |
   |            |     /     2\     2           2   /     2\        |           2          6*|x - -------|*log(7)|
 x |   3        \     \1 + x /*acot (x)   1 + x    \1 + x /*acot(x)/      3*log (7)         \    acot(x)/       |
7 *|log (7) + ------------------------------------------------------ + ---------------- - ----------------------|
   |                                    2                              /     2\                     2           |
   |                            /     2\                               \1 + x /*acot(x)     /     2\            |
   \                            \1 + x / *acot(x)                                           \1 + x / *acot(x)   /
-----------------------------------------------------------------------------------------------------------------
                                                     acot(x)
7x(−6(x−1acot⁡(x))log⁡(7)(x2+1)2acot⁡(x)+log⁡(7)3+3log⁡(7)2(x2+1)acot⁡(x)+2(4x2x2+1−6x(x2+1)acot⁡(x)−1+3(x2+1)acot⁡2(x))(x2+1)2acot⁡(x))acot⁡(x)\frac{7^{x} \left(- \frac{6 \left(x - \frac{1}{\operatorname{acot}{\left(x \right)}}\right) \log{\left(7 \right)}}{\left(x^{2} + 1\right)^{2} \operatorname{acot}{\left(x \right)}} + \log{\left(7 \right)}^{3} + \frac{3 \log{\left(7 \right)}^{2}}{\left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}} + \frac{2 \left(\frac{4 x^{2}}{x^{2} + 1} - \frac{6 x}{\left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}} - 1 + \frac{3}{\left(x^{2} + 1\right) \operatorname{acot}^{2}{\left(x \right)}}\right)}{\left(x^{2} + 1\right)^{2} \operatorname{acot}{\left(x \right)}}\right)}{\operatorname{acot}{\left(x \right)}}
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Gráfico
Derivada de y=7^x/arctgx
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