Господин Экзамен
Производная asin(a*sin(x))
Решение
Вы ввели
[src]
asin(a*sin(x))
$$\operatorname{asin}{\left(a \sin{\left(x \right)} \right)}$$
d --(asin(a*sin(x))) dx
$$\frac{\partial}{\partial x} \operatorname{asin}{\left(a \sin{\left(x \right)} \right)}$$
Первая производная
[src]
a*cos(x) ------------------- ________________ / 2 2 \/ 1 - a *sin (x)
$$\frac{a \cos{\left(x \right)}}{\sqrt{- a^{2} \sin^{2}{\left(x \right)} + 1}}$$
Вторая производная
[src]
/ 2 2 \
| a *cos (x) |
a*|-1 + --------------|*sin(x)
| 2 2 |
\ 1 - a *sin (x)/
------------------------------
________________
/ 2 2
\/ 1 - a *sin (x)
$$\frac{a \left(\frac{a^{2} \cos^{2}{\left(x \right)}}{- a^{2} \sin^{2}{\left(x \right)} + 1} - 1\right) \sin{\left(x \right)}}{\sqrt{- a^{2} \sin^{2}{\left(x \right)} + 1}}$$
Третья производная
[src]
/ 2 2 2 2 4 2 2 \
| a *cos (x) 3*a *sin (x) 3*a *cos (x)*sin (x)|
a*|-1 + -------------- - -------------- + --------------------|*cos(x)
| 2 2 2 2 2 |
| 1 - a *sin (x) 1 - a *sin (x) / 2 2 \ |
\ \1 - a *sin (x)/ /
----------------------------------------------------------------------
________________
/ 2 2
\/ 1 - a *sin (x)
$$\frac{a \left(\frac{3 a^{4} \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)}}{\left(- a^{2} \sin^{2}{\left(x \right)} + 1\right)^{2}} - \frac{3 a^{2} \sin^{2}{\left(x \right)}}{- a^{2} \sin^{2}{\left(x \right)} + 1} + \frac{a^{2} \cos^{2}{\left(x \right)}}{- a^{2} \sin^{2}{\left(x \right)} + 1} - 1\right) \cos{\left(x \right)}}{\sqrt{- a^{2} \sin^{2}{\left(x \right)} + 1}}$$