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y=arctg(x/√(9-x))
Derivada de la función/ √(9-x)/ arctg/ y=arctg(x/√(9-x))

Derivada de y=arctg(x/√(9-x))

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

Gráfico:

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Solución

Ha introducido [src] 
    /    x    \
atan|---------|
    |  _______|
    \\/ 9 - x /
atan⁡(x9−x)\operatorname{atan}{\left(\frac{x}{\sqrt{9 - x}} \right)} 
atan(x/sqrt(9 - x))
Gráfica
02468-8-6-4-2-10102.5-2.5
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
    1            x      
--------- + ------------
  _______            3/2
\/ 9 - x    2*(9 - x)   
------------------------
              2         
             x          
       1 + -----        
           9 - x
x2(9−x)32+19−xx29−x+1\frac{\frac{x}{2 \left(9 - x\right)^{\frac{3}{2}}} + \frac{1}{\sqrt{9 - x}}}{\frac{x^{2}}{9 - x} + 1}
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Segunda derivada [src] 
 /                                  /       x   \ /      x  \\ 
 |                              2*x*|-2 + ------|*|2 + -----|| 
 |    2        2       3*x          \     -9 + x/ \    9 - x/| 
-|- ------ + ----- + -------- + -----------------------------| 
 |  -9 + x   9 - x          2       /        2  \            | 
 |                   (9 - x)        |       x   |            | 
 |                                  |-1 + ------|*(-9 + x)   | 
 \                                  \     -9 + x/            / 
---------------------------------------------------------------
                     /        2  \                             
                     |       x   |   _______                   
                   4*|-1 + ------|*\/ 9 - x                    
                     \     -9 + x/
−2x(x9−x+2)(xx−9−2)(x−9)(x2x−9−1)+3x(9−x)2−2x−9+29−x49−x(x2x−9−1)- \frac{\frac{2 x \left(\frac{x}{9 - x} + 2\right) \left(\frac{x}{x - 9} - 2\right)}{\left(x - 9\right) \left(\frac{x^{2}}{x - 9} - 1\right)} + \frac{3 x}{\left(9 - x\right)^{2}} - \frac{2}{x - 9} + \frac{2}{9 - x}}{4 \sqrt{9 - x} \left(\frac{x^{2}}{x - 9} - 1\right)}
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Tercera derivada [src] 
                              /         2            \                                                                                
                  /      x  \ |        x        2*x  |                   2                 /       x   \ /    2        2       3*x   \
    /     5*x \   |2 + -----|*|1 + --------- - ------|    2 /       x   \  /      x  \   x*|-2 + ------|*|- ------ + ----- + --------|
  3*|6 + -----|   \    9 - x/ |            2   -9 + x|   x *|-2 + ------| *|2 + -----|     \     -9 + x/ |  -9 + x   9 - x          2|
    \    9 - x/               \    (-9 + x)          /      \     -9 + x/  \    9 - x/                   \                   (9 - x) /
- ------------- + ------------------------------------ - ----------------------------- - ---------------------------------------------
             2           /        2  \                                   2                            /        2  \                   
    8*(9 - x)            |       x   |                      /        2  \                             |       x   |                   
                         |-1 + ------|*(-9 + x)             |       x   |          2                2*|-1 + ------|*(-9 + x)          
                         \     -9 + x/                      |-1 + ------| *(-9 + x)                   \     -9 + x/                   
                                                            \     -9 + x/                                                             
--------------------------------------------------------------------------------------------------------------------------------------
                                                       /        2  \                                                                  
                                                       |       x   |   _______                                                        
                                                       |-1 + ------|*\/ 9 - x                                                         
                                                       \     -9 + x/
−x2(x9−x+2)(xx−9−2)2(x−9)2(x2x−9−1)2−x(xx−9−2)(3x(9−x)2−2x−9+29−x)2(x−9)(x2x−9−1)+(x9−x+2)(x2(x−9)2−2xx−9+1)(x−9)(x2x−9−1)−3(5x9−x+6)8(9−x)29−x(x2x−9−1)\frac{- \frac{x^{2} \left(\frac{x}{9 - x} + 2\right) \left(\frac{x}{x - 9} - 2\right)^{2}}{\left(x - 9\right)^{2} \left(\frac{x^{2}}{x - 9} - 1\right)^{2}} - \frac{x \left(\frac{x}{x - 9} - 2\right) \left(\frac{3 x}{\left(9 - x\right)^{2}} - \frac{2}{x - 9} + \frac{2}{9 - x}\right)}{2 \left(x - 9\right) \left(\frac{x^{2}}{x - 9} - 1\right)} + \frac{\left(\frac{x}{9 - x} + 2\right) \left(\frac{x^{2}}{\left(x - 9\right)^{2}} - \frac{2 x}{x - 9} + 1\right)}{\left(x - 9\right) \left(\frac{x^{2}}{x - 9} - 1\right)} - \frac{3 \left(\frac{5 x}{9 - x} + 6\right)}{8 \left(9 - x\right)^{2}}}{\sqrt{9 - x} \left(\frac{x^{2}}{x - 9} - 1\right)}
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Gráfico
Derivada de y=arctg(x/√(9-x))
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