Производная sin(x)*acos(x)

Вы ввели

sin(x)*acos(x)

$$\sin{\left(x \right)} \operatorname{acos}{\left(x \right)}$$

d                 
--(sin(x)*acos(x))
dx                

$$\frac{d}{d x} \sin{\left(x \right)} \operatorname{acos}{\left(x \right)}$$

Первая производная

                    sin(x)  
acos(x)*cos(x) - -----------
                    ________
                   /      2 
                 \/  1 - x  

$$\cos{\left(x \right)} \operatorname{acos}{\left(x \right)} - \frac{\sin{\left(x \right)}}{\sqrt{1 - x^{2}}}$$

Вторая производная

 /                   2*cos(x)      x*sin(x) \
-|acos(x)*sin(x) + ----------- + -----------|
 |                    ________           3/2|
 |                   /      2    /     2\   |
 \                 \/  1 - x     \1 - x /   /

$$- (\frac{x \sin{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \sin{\left(x \right)} \operatorname{acos}{\left(x \right)} + \frac{2 \cos{\left(x \right)}}{\sqrt{1 - x^{2}}})$$

Третья производная

                                /          2 \                     
                                |       3*x  |                     
                                |-1 + -------|*sin(x)              
                                |           2|                     
                    3*sin(x)    \     -1 + x /           3*x*cos(x)
-acos(x)*cos(x) + ----------- + --------------------- - -----------
                     ________                3/2                3/2
                    /      2         /     2\           /     2\   
                  \/  1 - x          \1 - x /           \1 - x /   

$$- \frac{3 x \cos{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \cos{\left(x \right)} \operatorname{acos}{\left(x \right)} + \frac{3 \sin{\left(x \right)}}{\sqrt{1 - x^{2}}} + \frac{\left(\frac{3 x^{2}}{x^{2} - 1} - 1\right) \sin{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}}$$

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