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y=sin^2(5^(2x-1)-arctgx)
Derivada de la función/ sin^2/ arctg/ y=sin/ (2x-1)/ y=sin^2(5^(2x-1)-arctgx)

Derivada de y=sin^2(5^(2x-1)-arctgx)

Función f() - derivada -er orden en el punto
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Gráfico:

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Solución

Ha introducido [src] 
   2/ 2*x - 1          \
sin \5        - acot(x)/
sin⁡2(52x−1−acot⁡(x))\sin^{2}{\left(5^{2 x - 1} - \operatorname{acot}{\left(x \right)} \right)} 
sin(5^(2*x - 1) - acot(x))^2
Gráfica
02468-8-6-4-2-1010-2000000000000020000000000000
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Primera derivada [src] 
  /  1         2*x - 1       \    / 2*x - 1          \    / 2*x - 1          \
2*|------ + 2*5       *log(5)|*cos\5        - acot(x)/*sin\5        - acot(x)/
  |     2                    |                                                
  \1 + x                     /
2(2⋅52x−1log⁡(5)+1x2+1)sin⁡(52x−1−acot⁡(x))cos⁡(52x−1−acot⁡(x))2 \left(2 \cdot 5^{2 x - 1} \log{\left(5 \right)} + \frac{1}{x^{2} + 1}\right) \sin{\left(5^{2 x - 1} - \operatorname{acot}{\left(x \right)} \right)} \cos{\left(5^{2 x - 1} - \operatorname{acot}{\left(x \right)} \right)}
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Segunda derivada [src] 
  /                        2     /            2*x\                           2     /            2*x\                                        /            2*x\    /            2*x\\
  |/  5         2*x       \     2|           5   |   /  5         2*x       \     2|           5   |      /     5*x         2*x    2   \    |           5   |    |           5   ||
2*||------ + 2*5   *log(5)| *cos |-acot(x) + ----| - |------ + 2*5   *log(5)| *sin |-acot(x) + ----| + 10*|- --------- + 2*5   *log (5)|*cos|-acot(x) + ----|*sin|-acot(x) + ----||
  ||     2                |      \            5  /   |     2                |      \            5  /      |          2                 |    \            5  /    \            5  /|
  |\1 + x                 /                          \1 + x                 /                             |  /     2\                  |                                          |
  \                                                                                                       \  \1 + x /                  /                                          /
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                                                                                         25
2(−(2⋅52xlog⁡(5)+5x2+1)2sin⁡2(52x5−acot⁡(x))+(2⋅52xlog⁡(5)+5x2+1)2cos⁡2(52x5−acot⁡(x))+10(2⋅52xlog⁡(5)2−5x(x2+1)2)sin⁡(52x5−acot⁡(x))cos⁡(52x5−acot⁡(x)))25\frac{2 \left(- \left(2 \cdot 5^{2 x} \log{\left(5 \right)} + \frac{5}{x^{2} + 1}\right)^{2} \sin^{2}{\left(\frac{5^{2 x}}{5} - \operatorname{acot}{\left(x \right)} \right)} + \left(2 \cdot 5^{2 x} \log{\left(5 \right)} + \frac{5}{x^{2} + 1}\right)^{2} \cos^{2}{\left(\frac{5^{2 x}}{5} - \operatorname{acot}{\left(x \right)} \right)} + 10 \left(2 \cdot 5^{2 x} \log{\left(5 \right)}^{2} - \frac{5 x}{\left(x^{2} + 1\right)^{2}}\right) \sin{\left(\frac{5^{2 x}}{5} - \operatorname{acot}{\left(x \right)} \right)} \cos{\left(\frac{5^{2 x}}{5} - \operatorname{acot}{\left(x \right)} \right)}\right)}{25}
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Tercera derivada [src] 
  /         /            2*x\                                                                                     3    /            2*x\    /            2*x\          /            2*x\                                                              /                                     2  \    /            2*x\    /            2*x\\
  |        2|           5   | /  5         2*x       \ /     5*x         2*x    2   \     /  5         2*x       \     |           5   |    |           5   |         2|           5   | /  5         2*x       \ /     5*x         2*x    2   \      |      5          2*x    3        20*x   |    |           5   |    |           5   ||
4*|- 15*sin |-acot(x) + ----|*|------ + 2*5   *log(5)|*|- --------- + 2*5   *log (5)| - 2*|------ + 2*5   *log(5)| *cos|-acot(x) + ----|*sin|-acot(x) + ----| + 15*cos |-acot(x) + ----|*|------ + 2*5   *log(5)|*|- --------- + 2*5   *log (5)| + 25*|- --------- + 4*5   *log (5) + ---------|*cos|-acot(x) + ----|*sin|-acot(x) + ----||
  |         \            5  / |     2                | |          2                 |     |     2                |     \            5  /    \            5  /          \            5  / |     2                | |          2                 |      |          2                            3|    \            5  /    \            5  /|
  |                           \1 + x                 / |  /     2\                  |     \1 + x                 /                                                                       \1 + x                 / |  /     2\                  |      |  /     2\                     /     2\ |                                          |
  \                                                    \  \1 + x /                  /                                                                                                                             \  \1 + x /                  /      \  \1 + x /                     \1 + x / /                                          /
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                                                                                                                                                                    125
4(−2(2⋅52xlog⁡(5)+5x2+1)3sin⁡(52x5−acot⁡(x))cos⁡(52x5−acot⁡(x))−15(2⋅52xlog⁡(5)+5x2+1)(2⋅52xlog⁡(5)2−5x(x2+1)2)sin⁡2(52x5−acot⁡(x))+15(2⋅52xlog⁡(5)+5x2+1)(2⋅52xlog⁡(5)2−5x(x2+1)2)cos⁡2(52x5−acot⁡(x))+25(4⋅52xlog⁡(5)3+20x2(x2+1)3−5(x2+1)2)sin⁡(52x5−acot⁡(x))cos⁡(52x5−acot⁡(x)))125\frac{4 \left(- 2 \left(2 \cdot 5^{2 x} \log{\left(5 \right)} + \frac{5}{x^{2} + 1}\right)^{3} \sin{\left(\frac{5^{2 x}}{5} - \operatorname{acot}{\left(x \right)} \right)} \cos{\left(\frac{5^{2 x}}{5} - \operatorname{acot}{\left(x \right)} \right)} - 15 \left(2 \cdot 5^{2 x} \log{\left(5 \right)} + \frac{5}{x^{2} + 1}\right) \left(2 \cdot 5^{2 x} \log{\left(5 \right)}^{2} - \frac{5 x}{\left(x^{2} + 1\right)^{2}}\right) \sin^{2}{\left(\frac{5^{2 x}}{5} - \operatorname{acot}{\left(x \right)} \right)} + 15 \left(2 \cdot 5^{2 x} \log{\left(5 \right)} + \frac{5}{x^{2} + 1}\right) \left(2 \cdot 5^{2 x} \log{\left(5 \right)}^{2} - \frac{5 x}{\left(x^{2} + 1\right)^{2}}\right) \cos^{2}{\left(\frac{5^{2 x}}{5} - \operatorname{acot}{\left(x \right)} \right)} + 25 \left(4 \cdot 5^{2 x} \log{\left(5 \right)}^{3} + \frac{20 x^{2}}{\left(x^{2} + 1\right)^{3}} - \frac{5}{\left(x^{2} + 1\right)^{2}}\right) \sin{\left(\frac{5^{2 x}}{5} - \operatorname{acot}{\left(x \right)} \right)} \cos{\left(\frac{5^{2 x}}{5} - \operatorname{acot}{\left(x \right)} \right)}\right)}{125}
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Gráfico
Derivada de y=sin^2(5^(2x-1)-arctgx)
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