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The derivative of the function/ z(u,v)=atan(u/v)

Derivative of z(u,v)=atan(u/v)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
    /u\
atan|-|
    \v/
$$\operatorname{atan}{\left(\frac{u}{v} \right)}$$ 
atan(u/v)
The first derivative [src] 
    -u     
-----------
   /     2\
 2 |    u |
v *|1 + --|
   |     2|
   \    v /
$$- \frac{u}{v^{2} \left(\frac{u^{2}}{v^{2}} + 1\right)}$$
Simplify
The second derivative [src] 
    /          2    \
    |         u     |
2*u*|1 - -----------|
    |       /     2\|
    |     2 |    u ||
    |    v *|1 + --||
    |       |     2||
    \       \    v //
---------------------
        /     2\     
      3 |    u |     
     v *|1 + --|     
        |     2|     
        \    v /
$$\frac{2 u \left(- \frac{u^{2}}{v^{2} \left(\frac{u^{2}}{v^{2}} + 1\right)} + 1\right)}{v^{3} \left(\frac{u^{2}}{v^{2}} + 1\right)}$$
Simplify
The third derivative [src] 
    /            4              2   \
    |         4*u            7*u    |
2*u*|-3 - ------------ + -----------|
    |                2      /     2\|
    |        /     2\     2 |    u ||
    |      4 |    u |    v *|1 + --||
    |     v *|1 + --|       |     2||
    |        |     2|       \    v /|
    \        \    v /               /
-------------------------------------
                /     2\             
              4 |    u |             
             v *|1 + --|             
                |     2|             
                \    v /
$$\frac{2 u \left(- \frac{4 u^{4}}{v^{4} \left(\frac{u^{2}}{v^{2}} + 1\right)^{2}} + \frac{7 u^{2}}{v^{2} \left(\frac{u^{2}}{v^{2}} + 1\right)} - 3\right)}{v^{4} \left(\frac{u^{2}}{v^{2}} + 1\right)}$$
Simplify
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