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The derivative of the function/ atan(bx)

Derivative of atan(bx)

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

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from to

Piecewise:

The solution

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