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y=2^arctg(2x)+(ctg^3*x)^4

Derivada de y=2^arctg(2x)+(ctg^3*x)^4

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

Gráfico:

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Solución

Ha introducido [src]
                    4
 atan(2*x)      3    
2          + cot (x) 
$$2^{\operatorname{atan}{\left(2 x \right)}} + \left(\cot^{3}{\left(x \right)}\right)^{4}$$
2^atan(2*x) + (cot(x)^3)^4
Gráfica
Primera derivada [src]
   atan(2*x)               12    /          2   \
2*2         *log(2)   4*cot  (x)*\-3 - 3*cot (x)/
------------------- + ---------------------------
             2                   cot(x)          
      1 + 4*x                                    
$$\frac{2 \cdot 2^{\operatorname{atan}{\left(2 x \right)}} \log{\left(2 \right)}}{4 x^{2} + 1} + \frac{4 \left(- 3 \cot^{2}{\left(x \right)} - 3\right) \cot^{12}{\left(x \right)}}{\cot{\left(x \right)}}$$
Segunda derivada [src]
  /                                           2             atan(2*x)    2           atan(2*x)       \
  |     12    /       2   \      /       2   \     10      2         *log (2)   4*x*2         *log(2)|
4*|6*cot  (x)*\1 + cot (x)/ + 33*\1 + cot (x)/ *cot  (x) + ------------------ - ---------------------|
  |                                                                     2                      2     |
  |                                                           /       2\             /       2\      |
  \                                                           \1 + 4*x /             \1 + 4*x /      /
$$4 \left(- \frac{4 \cdot 2^{\operatorname{atan}{\left(2 x \right)}} x \log{\left(2 \right)}}{\left(4 x^{2} + 1\right)^{2}} + \frac{2^{\operatorname{atan}{\left(2 x \right)}} \log{\left(2 \right)}^{2}}{\left(4 x^{2} + 1\right)^{2}} + 33 \left(\cot^{2}{\left(x \right)} + 1\right)^{2} \cot^{10}{\left(x \right)} + 6 \left(\cot^{2}{\left(x \right)} + 1\right) \cot^{12}{\left(x \right)}\right)$$
Tercera derivada [src]
  /                   3                            2                                        atan(2*x)    3         atan(2*x)                atan(2*x)    2          atan(2*x)  2       \
  |      /       2   \     9          /       2   \     11           13    /       2   \   2         *log (2)   2*2         *log(2)   12*x*2         *log (2)   32*2         *x *log(2)|
8*|- 165*\1 + cot (x)/ *cot (x) - 102*\1 + cot (x)/ *cot  (x) - 6*cot  (x)*\1 + cot (x)/ + ------------------ - ------------------- - ----------------------- + -----------------------|
  |                                                                                                     3                     2                       3                         3      |
  |                                                                                           /       2\            /       2\              /       2\                /       2\       |
  \                                                                                           \1 + 4*x /            \1 + 4*x /              \1 + 4*x /                \1 + 4*x /       /
$$8 \left(\frac{32 \cdot 2^{\operatorname{atan}{\left(2 x \right)}} x^{2} \log{\left(2 \right)}}{\left(4 x^{2} + 1\right)^{3}} - \frac{12 \cdot 2^{\operatorname{atan}{\left(2 x \right)}} x \log{\left(2 \right)}^{2}}{\left(4 x^{2} + 1\right)^{3}} - \frac{2 \cdot 2^{\operatorname{atan}{\left(2 x \right)}} \log{\left(2 \right)}}{\left(4 x^{2} + 1\right)^{2}} + \frac{2^{\operatorname{atan}{\left(2 x \right)}} \log{\left(2 \right)}^{3}}{\left(4 x^{2} + 1\right)^{3}} - 165 \left(\cot^{2}{\left(x \right)} + 1\right)^{3} \cot^{9}{\left(x \right)} - 102 \left(\cot^{2}{\left(x \right)} + 1\right)^{2} \cot^{11}{\left(x \right)} - 6 \left(\cot^{2}{\left(x \right)} + 1\right) \cot^{13}{\left(x \right)}\right)$$
Gráfico
Derivada de y=2^arctg(2x)+(ctg^3*x)^4