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y=5*arcsinx*arctgx
Derivada de la función/ arcsin/ arctg/ y=5*arcsinx*arctgx

Derivada de y=5*arcsinx*arctgx

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

Ha introducido [src] 
5*asin(x)*acot(x)
acot⁡(x)5asin⁡(x)\operatorname{acot}{\left(x \right)} 5 \operatorname{asin}{\left(x \right)} 
(5*asin(x))*acot(x)
Gráfica
02468-8-6-4-2-1010-2020
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Primera derivada [src] 
  5*asin(x)    5*acot(x) 
- --------- + -----------
         2       ________
    1 + x       /      2 
              \/  1 - x
−5asin⁡(x)x2+1+5acot⁡(x)1−x2- \frac{5 \operatorname{asin}{\left(x \right)}}{x^{2} + 1} + \frac{5 \operatorname{acot}{\left(x \right)}}{\sqrt{1 - x^{2}}}
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Segunda derivada [src] 
  /           2              x*acot(x)    2*x*asin(x)\
5*|- -------------------- + ----------- + -----------|
  |              ________           3/2            2 |
  |  /     2\   /      2    /     2\       /     2\  |
  \  \1 + x /*\/  1 - x     \1 - x /       \1 + x /  /
5(2xasin⁡(x)(x2+1)2+xacot⁡(x)(1−x2)32−21−x2(x2+1))5 \left(\frac{2 x \operatorname{asin}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{x \operatorname{acot}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{2}{\sqrt{1 - x^{2}} \left(x^{2} + 1\right)}\right)
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Tercera derivada [src] 
  /  /          2 \                                    /         2 \                                \
  |  |       3*x  |                                    |      4*x  |                                |
  |  |-1 + -------|*acot(x)                          2*|-1 + ------|*asin(x)                        |
  |  |           2|                                    |          2|                                |
  |  \     -1 + x /                   3*x              \     1 + x /                    6*x         |
5*|- ---------------------- - -------------------- - ----------------------- + ---------------------|
  |               3/2                          3/2                  2                  2    ________|
  |       /     2\            /     2\ /     2\             /     2\           /     2\    /      2 |
  \       \1 - x /            \1 + x /*\1 - x /             \1 + x /           \1 + x / *\/  1 - x  /
5(6x1−x2(x2+1)2−3x(1−x2)32(x2+1)−2(4x2x2+1−1)asin⁡(x)(x2+1)2−(3x2x2−1−1)acot⁡(x)(1−x2)32)5 \left(\frac{6 x}{\sqrt{1 - x^{2}} \left(x^{2} + 1\right)^{2}} - \frac{3 x}{\left(1 - x^{2}\right)^{\frac{3}{2}} \left(x^{2} + 1\right)} - \frac{2 \left(\frac{4 x^{2}}{x^{2} + 1} - 1\right) \operatorname{asin}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{\left(\frac{3 x^{2}}{x^{2} - 1} - 1\right) \operatorname{acot}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}}\right)
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Gráfico
Derivada de y=5*arcsinx*arctgx
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