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y=t*arctg(t)
The derivative of the function/ y=t*arctg(t)

Derivative of y=t*arctg(t)

Function f() - derivative -N order at the point
v

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from to

Piecewise:

The solution

You have entered [src] 
t*atan(t)
$$t \operatorname{atan}{\left(t \right)}$$ 
t*atan(t)
The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
  t             
------ + atan(t)
     2          
1 + t
$$\frac{t}{t^{2} + 1} + \operatorname{atan}{\left(t \right)}$$
Simplify
The second derivative [src] 
  /       2  \
  |      t   |
2*|1 - ------|
  |         2|
  \    1 + t /
--------------
         2    
    1 + t
$$\frac{2 \left(- \frac{t^{2}}{t^{2} + 1} + 1\right)}{t^{2} + 1}$$
Simplify
The third derivative [src] 
    /         2 \
    |      4*t  |
2*t*|-4 + ------|
    |          2|
    \     1 + t /
-----------------
            2    
    /     2\     
    \1 + t /
$$\frac{2 t \left(\frac{4 t^{2}}{t^{2} + 1} - 4\right)}{\left(t^{2} + 1\right)^{2}}$$
Simplify
The graph
Derivative of y=t*arctg(t)
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