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y=(ctg-1)(cosx+2ctgx)

Derivada de y=(ctg-1)(cosx+2ctgx)

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Solución

Ha introducido [src]
(cot(x) - 1)*(cos(x) + 2*cot(x))
$$\left(\cos{\left(x \right)} + 2 \cot{\left(x \right)}\right) \left(\cot{\left(x \right)} - 1\right)$$
(cot(x) - 1)*(cos(x) + 2*cot(x))
Gráfica
Primera derivada [src]
/        2   \                                    /                   2   \
\-1 - cot (x)/*(cos(x) + 2*cot(x)) + (cot(x) - 1)*\-2 - sin(x) - 2*cot (x)/
$$\left(\cos{\left(x \right)} + 2 \cot{\left(x \right)}\right) \left(- \cot^{2}{\left(x \right)} - 1\right) + \left(\cot{\left(x \right)} - 1\right) \left(- \sin{\left(x \right)} - 2 \cot^{2}{\left(x \right)} - 2\right)$$
Segunda derivada [src]
              /            /       2   \       \     /       2   \ /         2            \     /       2   \                           
(-1 + cot(x))*\-cos(x) + 4*\1 + cot (x)/*cot(x)/ + 2*\1 + cot (x)/*\2 + 2*cot (x) + sin(x)/ + 2*\1 + cot (x)/*(2*cot(x) + cos(x))*cot(x)
$$\left(4 \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)} - \cos{\left(x \right)}\right) \left(\cot{\left(x \right)} - 1\right) + 2 \left(\cos{\left(x \right)} + 2 \cot{\left(x \right)}\right) \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)} + 2 \left(\cot^{2}{\left(x \right)} + 1\right) \left(\sin{\left(x \right)} + 2 \cot^{2}{\left(x \right)} + 2\right)$$
Tercera derivada [src]
 /              /                         2                          \                                                                                                                                                             \
 |              |            /       2   \         2    /       2   \|     /       2   \ /            /       2   \       \     /       2   \ /         2   \                         /       2   \ /         2            \       |
-\(-1 + cot(x))*\-sin(x) + 4*\1 + cot (x)/  + 8*cot (x)*\1 + cot (x)// + 3*\1 + cot (x)/*\-cos(x) + 4*\1 + cot (x)/*cot(x)/ + 2*\1 + cot (x)/*\1 + 3*cot (x)/*(2*cot(x) + cos(x)) + 6*\1 + cot (x)/*\2 + 2*cot (x) + sin(x)/*cot(x)/
$$- (3 \left(4 \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)} - \cos{\left(x \right)}\right) \left(\cot^{2}{\left(x \right)} + 1\right) + 2 \left(\cos{\left(x \right)} + 2 \cot{\left(x \right)}\right) \left(\cot^{2}{\left(x \right)} + 1\right) \left(3 \cot^{2}{\left(x \right)} + 1\right) + \left(\cot{\left(x \right)} - 1\right) \left(4 \left(\cot^{2}{\left(x \right)} + 1\right)^{2} + 8 \left(\cot^{2}{\left(x \right)} + 1\right) \cot^{2}{\left(x \right)} - \sin{\left(x \right)}\right) + 6 \left(\cot^{2}{\left(x \right)} + 1\right) \left(\sin{\left(x \right)} + 2 \cot^{2}{\left(x \right)} + 2\right) \cot{\left(x \right)})$$
Gráfico
Derivada de y=(ctg-1)(cosx+2ctgx)