Mister Exam

Other calculators

The derivative of the function/ atan(y+2-y^2)

Derivative of atan(y+2-y^2)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
    /         2\
atan\y + 2 - y /
atan⁡(−y2+(y+2))\operatorname{atan}{\left(- y^{2} + \left(y + 2\right) \right)} 
atan(y + 2 - y^2)
The graph
02468-8-6-4-2-10105-5
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
     1 - 2*y     
-----------------
                2
    /         2\ 
1 + \y + 2 - y /
1−2y(−y2+(y+2))2+1\frac{1 - 2 y}{\left(- y^{2} + \left(y + 2\right)\right)^{2} + 1}
Simplify
The second derivative [src] 
   /              2 /         2\\
   |    (-1 + 2*y) *\2 + y - y /|
-2*|1 + ------------------------|
   |                       2    |
   |           /         2\     |
   \       1 + \2 + y - y /     /
---------------------------------
                        2        
            /         2\         
        1 + \2 + y - y /
−2((2y−1)2(−y2+y+2)(−y2+y+2)2+1+1)(−y2+y+2)2+1- \frac{2 \left(\frac{\left(2 y - 1\right)^{2} \left(- y^{2} + y + 2\right)}{\left(- y^{2} + y + 2\right)^{2} + 1} + 1\right)}{\left(- y^{2} + y + 2\right)^{2} + 1}
Simplify
The third derivative [src] 
             /                                                           2\
             |                                             2 /         2\ |
             |                2            2   4*(-1 + 2*y) *\2 + y - y / |
2*(-1 + 2*y)*|-12 + (-1 + 2*y)  - 6*y + 6*y  - ---------------------------|
             |                                                      2     |
             |                                          /         2\      |
             \                                      1 + \2 + y - y /      /
---------------------------------------------------------------------------
                                               2                           
                            /                2\                            
                            |    /         2\ |                            
                            \1 + \2 + y - y / /
2(2y−1)(6y2−6y+(2y−1)2−4(2y−1)2(−y2+y+2)2(−y2+y+2)2+1−12)((−y2+y+2)2+1)2\frac{2 \left(2 y - 1\right) \left(6 y^{2} - 6 y + \left(2 y - 1\right)^{2} - \frac{4 \left(2 y - 1\right)^{2} \left(- y^{2} + y + 2\right)^{2}}{\left(- y^{2} + y + 2\right)^{2} + 1} - 12\right)}{\left(\left(- y^{2} + y + 2\right)^{2} + 1\right)^{2}}
Simplify
    © Mister Exam – Calculator