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y=10^x*arcctg(2x)
Derivada de la función/ tg(2x)/ y=10^x/ y=10^x*arcctg(2x)

Derivada de y=10^x*arcctg(2x)

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

Ha introducido [src] 
  x          
10 *acot(2*x)
10xacot⁡(2x)10^{x} \operatorname{acot}{\left(2 x \right)} 
10^x*acot(2*x)
Gráfica
02468-8-6-4-2-10102000000000-1000000000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
       x                          
   2*10        x                  
- -------- + 10 *acot(2*x)*log(10)
         2                        
  1 + 4*x
10xlog⁡(10)acot⁡(2x)−2⋅10x4x2+110^{x} \log{\left(10 \right)} \operatorname{acot}{\left(2 x \right)} - \frac{2 \cdot 10^{x}}{4 x^{2} + 1}
Simplificar
Segunda derivada [src] 
  x /   2                 4*log(10)       16*x   \
10 *|log (10)*acot(2*x) - --------- + -----------|
    |                             2             2|
    |                      1 + 4*x    /       2\ |
    \                                 \1 + 4*x / /
10x(16x(4x2+1)2+log⁡(10)2acot⁡(2x)−4log⁡(10)4x2+1)10^{x} \left(\frac{16 x}{\left(4 x^{2} + 1\right)^{2}} + \log{\left(10 \right)}^{2} \operatorname{acot}{\left(2 x \right)} - \frac{4 \log{\left(10 \right)}}{4 x^{2} + 1}\right)
Simplificar
Tercera derivada [src] 
    /                        /          2  \                            \
    |                        |      16*x   |                            |
    |                     16*|-1 + --------|                            |
    |                        |            2|        2                   |
  x |   3                    \     1 + 4*x /   6*log (10)   48*x*log(10)|
10 *|log (10)*acot(2*x) - ------------------ - ---------- + ------------|
    |                                  2               2              2 |
    |                        /       2\         1 + 4*x     /       2\  |
    \                        \1 + 4*x /                     \1 + 4*x /  /
10x(48xlog⁡(10)(4x2+1)2+log⁡(10)3acot⁡(2x)−6log⁡(10)24x2+1−16(16x24x2+1−1)(4x2+1)2)10^{x} \left(\frac{48 x \log{\left(10 \right)}}{\left(4 x^{2} + 1\right)^{2}} + \log{\left(10 \right)}^{3} \operatorname{acot}{\left(2 x \right)} - \frac{6 \log{\left(10 \right)}^{2}}{4 x^{2} + 1} - \frac{16 \left(\frac{16 x^{2}}{4 x^{2} + 1} - 1\right)}{\left(4 x^{2} + 1\right)^{2}}\right)
Simplificar
Gráfico
Derivada de y=10^x*arcctg(2x)
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