Sr Examen

Derivada de y=2arcsinx+2ctgx-5x

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

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Solución

Ha introducido [src]
2*asin(x) + 2*cot(x) - 5*x
$$- 5 x + \left(2 \cot{\left(x \right)} + 2 \operatorname{asin}{\left(x \right)}\right)$$
2*asin(x) + 2*cot(x) - 5*x
Gráfica
Primera derivada [src]
          2           2     
-7 - 2*cot (x) + -----------
                    ________
                   /      2 
                 \/  1 - x  
$$- 2 \cot^{2}{\left(x \right)} - 7 + \frac{2}{\sqrt{1 - x^{2}}}$$
Segunda derivada [src]
  /     x          /       2   \       \
2*|----------- + 2*\1 + cot (x)/*cot(x)|
  |        3/2                         |
  |/     2\                            |
  \\1 - x /                            /
$$2 \left(\frac{x}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + 2 \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)}\right)$$
Tercera derivada [src]
  /                             2                                    2   \
  |     1          /       2   \         2    /       2   \       3*x    |
2*|----------- - 2*\1 + cot (x)/  - 4*cot (x)*\1 + cot (x)/ + -----------|
  |        3/2                                                        5/2|
  |/     2\                                                   /     2\   |
  \\1 - x /                                                   \1 - x /   /
$$2 \left(\frac{3 x^{2}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} - 2 \left(\cot^{2}{\left(x \right)} + 1\right)^{2} - 4 \left(\cot^{2}{\left(x \right)} + 1\right) \cot^{2}{\left(x \right)} + \frac{1}{\left(1 - x^{2}\right)^{\frac{3}{2}}}\right)$$
Gráfico
Derivada de y=2arcsinx+2ctgx-5x