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The derivative of the function/ t*arcsin(1-x)+arctg(x/2)

Derivative of t*arcsin(1-x)+arctg(x/2)

Function f() - derivative -N order at the point
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The solution

You have entered [src] 
                    /x\
t*asin(1 - x) + atan|-|
                    \2/
tasin⁡(1−x)+atan⁡(x2)t \operatorname{asin}{\left(1 - x \right)} + \operatorname{atan}{\left(\frac{x}{2} \right)} 
t*asin(1 - x) + atan(x/2)
The first derivative [src] 
    1                t        
---------- - -----------------
  /     2\      ______________
  |    x |     /            2 
2*|1 + --|   \/  1 - (1 - x)  
  \    4 /
−t1−(1−x)2+12(x24+1)- \frac{t}{\sqrt{1 - \left(1 - x\right)^{2}}} + \frac{1}{2 \left(\frac{x^{2}}{4} + 1\right)}
Simplify
The second derivative [src] 
 /   4*x          t*(-1 + x)   \
-|--------- + -----------------|
 |        2                 3/2|
 |/     2\    /           2\   |
 \\4 + x /    \1 - (1 - x) /   /
−(t(x−1)(1−(1−x)2)32+4x(x2+4)2)- (\frac{t \left(x - 1\right)}{\left(1 - \left(1 - x\right)^{2}\right)^{\frac{3}{2}}} + \frac{4 x}{\left(x^{2} + 4\right)^{2}})
Simplify
The third derivative [src] 
                                        2                   2  
      4               t             16*x        3*t*(-1 + x)   
- --------- - ----------------- + --------- - -----------------
          2                 3/2           3                 5/2
  /     2\    /           2\      /     2\    /           2\   
  \4 + x /    \1 - (1 - x) /      \4 + x /    \1 - (1 - x) /
−t(1−(1−x)2)32−3t(x−1)2(1−(1−x)2)52+16x2(x2+4)3−4(x2+4)2- \frac{t}{\left(1 - \left(1 - x\right)^{2}\right)^{\frac{3}{2}}} - \frac{3 t \left(x - 1\right)^{2}}{\left(1 - \left(1 - x\right)^{2}\right)^{\frac{5}{2}}} + \frac{16 x^{2}}{\left(x^{2} + 4\right)^{3}} - \frac{4}{\left(x^{2} + 4\right)^{2}}
Simplify
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