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y=3tsint+9ctgt-arctgt
Derivada de la función/ arctg/ tsint/ y=3tsint+9ctgt-arctgt

Derivada de y=3tsint+9ctgt-arctgt

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

Gráfico:

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Solución

Ha introducido [src] 
3*t*sin(t) + 9*cot(t) - atan(t)
(3tsin⁡(t)+9cot⁡(t))−atan⁡(t)\left(3 t \sin{\left(t \right)} + 9 \cot{\left(t \right)}\right) - \operatorname{atan}{\left(t \right)} 
(3*t)*sin(t) + 9*cot(t) - atan(t)
Gráfica
02468-8-6-4-2-1010-100000100000
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Trazar el gráfico f'(x)
Primera derivada [src] 
       1           2                           
-9 - ------ - 9*cot (t) + 3*sin(t) + 3*t*cos(t)
          2                                    
     1 + t
3tcos⁡(t)+3sin⁡(t)−9cot⁡2(t)−9−1t2+13 t \cos{\left(t \right)} + 3 \sin{\left(t \right)} - 9 \cot^{2}{\left(t \right)} - 9 - \frac{1}{t^{2} + 1}
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Segunda derivada [src] 
                           2*t         /       2   \       
6*cos(t) - 3*t*sin(t) + --------- + 18*\1 + cot (t)/*cot(t)
                                2                          
                        /     2\                           
                        \1 + t /
−3tsin⁡(t)+2t(t2+1)2+18(cot⁡2(t)+1)cot⁡(t)+6cos⁡(t)- 3 t \sin{\left(t \right)} + \frac{2 t}{\left(t^{2} + 1\right)^{2}} + 18 \left(\cot^{2}{\left(t \right)} + 1\right) \cot{\left(t \right)} + 6 \cos{\left(t \right)}
Simplificar
Tercera derivada [src] 
                  2                                                           2               
     /       2   \                   2             2    /       2   \      8*t                
- 18*\1 + cot (t)/  - 9*sin(t) + --------- - 36*cot (t)*\1 + cot (t)/ - --------- - 3*t*cos(t)
                                         2                                      3             
                                 /     2\                               /     2\              
                                 \1 + t /                               \1 + t /
−8t2(t2+1)3−3tcos⁡(t)−18(cot⁡2(t)+1)2−36(cot⁡2(t)+1)cot⁡2(t)−9sin⁡(t)+2(t2+1)2- \frac{8 t^{2}}{\left(t^{2} + 1\right)^{3}} - 3 t \cos{\left(t \right)} - 18 \left(\cot^{2}{\left(t \right)} + 1\right)^{2} - 36 \left(\cot^{2}{\left(t \right)} + 1\right) \cot^{2}{\left(t \right)} - 9 \sin{\left(t \right)} + \frac{2}{\left(t^{2} + 1\right)^{2}}
Simplificar
Gráfico
Derivada de y=3tsint+9ctgt-arctgt
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