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The derivative of the function/ (asint×acost)

Derivative of (asint×acost)

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

You have entered [src] 
asin(t)*acos(t)
acos⁡(t)asin⁡(t)\operatorname{acos}{\left(t \right)} \operatorname{asin}{\left(t \right)} 
asin(t)*acos(t)
The graph
02468-8-6-4-2-1010-1010
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
  acos(t)       asin(t)  
----------- - -----------
   ________      ________
  /      2      /      2 
\/  1 - t     \/  1 - t
acos⁡(t)1−t2−asin⁡(t)1−t2\frac{\operatorname{acos}{\left(t \right)}}{\sqrt{1 - t^{2}}} - \frac{\operatorname{asin}{\left(t \right)}}{\sqrt{1 - t^{2}}}
Simplify
The second derivative [src] 
   2       t*acos(t)     t*asin(t) 
------- + ----------- - -----------
      2           3/2           3/2
-1 + t    /     2\      /     2\   
          \1 - t /      \1 - t /
tacos⁡(t)(1−t2)32−tasin⁡(t)(1−t2)32+2t2−1\frac{t \operatorname{acos}{\left(t \right)}}{\left(1 - t^{2}\right)^{\frac{3}{2}}} - \frac{t \operatorname{asin}{\left(t \right)}}{\left(1 - t^{2}\right)^{\frac{3}{2}}} + \frac{2}{t^{2} - 1}
Simplify
The third derivative [src] 
               /          2 \           /          2 \        
               |       3*t  |           |       3*t  |        
               |-1 + -------|*asin(t)   |-1 + -------|*acos(t)
               |           2|           |           2|        
     6*t       \     -1 + t /           \     -1 + t /        
- ---------- + ---------------------- - ----------------------
           2                3/2                      3/2      
  /      2\         /     2\                 /     2\         
  \-1 + t /         \1 - t /                 \1 - t /
−6t(t2−1)2−(3t2t2−1−1)acos⁡(t)(1−t2)32+(3t2t2−1−1)asin⁡(t)(1−t2)32- \frac{6 t}{\left(t^{2} - 1\right)^{2}} - \frac{\left(\frac{3 t^{2}}{t^{2} - 1} - 1\right) \operatorname{acos}{\left(t \right)}}{\left(1 - t^{2}\right)^{\frac{3}{2}}} + \frac{\left(\frac{3 t^{2}}{t^{2} - 1} - 1\right) \operatorname{asin}{\left(t \right)}}{\left(1 - t^{2}\right)^{\frac{3}{2}}}
Simplify
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