Производная 2*asin((2*x-2)/sqrt(7))-5/4*sqrt(7-4*(x-1)^2)
Решение
Вы ввели
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________________
/ 2
/2*x - 2\ 5*\/ 7 - 4*(x - 1)
2*asin|-------| - ---------------------
| ___ | 4
\ \/ 7 /
$$- \frac{5}{4} \sqrt{- 4 \left(x - 1\right)^{2} + 7} + 2 \operatorname{asin}{\left (\frac{1}{\sqrt{7}} \left(2 x - 2\right) \right )}$$
График
Первая производная
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___
5*(4 - 4*x) 4*\/ 7
- --------------------- + -----------------------
________________ ________________
/ 2 / 2
4*\/ 7 - 4*(x - 1) / (2*x - 2)
7* / 1 - ----------
\/ 7
$$- \frac{- 20 x + 20}{4 \sqrt{- 4 \left(x - 1\right)^{2} + 7}} + \frac{4 \sqrt{7}}{7 \sqrt{- \frac{1}{7} \left(2 x - 2\right)^{2} + 1}}$$
Вторая производная
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2 ___
5 20*(-1 + x) 16*\/ 7 *(-1 + x)
-------------------- + -------------------- + -----------------------
_________________ 3/2 3/2
/ 2 / 2\ / 2\
\/ 7 - 4*(-1 + x) \7 - 4*(-1 + x) / | 4*(-1 + x) |
49*|1 - -----------|
\ 7 /
$$\frac{20 \left(x - 1\right)^{2}}{\left(- 4 \left(x - 1\right)^{2} + 7\right)^{\frac{3}{2}}} + \frac{16 \sqrt{7} \left(x - 1\right)}{49 \left(- \frac{4}{7} \left(x - 1\right)^{2} + 1\right)^{\frac{3}{2}}} + \frac{5}{\sqrt{- 4 \left(x - 1\right)^{2} + 7}}$$
Третья производная
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/ 3 ___ ___ 2 \ | 15*(-1 + x) 60*(-1 + x) 4*\/ 7 48*\/ 7 *(-1 + x) | 4*|-------------------- + -------------------- + ----------------------- + ------------------------| | 3/2 5/2 3/2 5/2| |/ 2\ / 2\ / 2\ / 2\ | |\7 - 4*(-1 + x) / \7 - 4*(-1 + x) / | 4*(-1 + x) | | 4*(-1 + x) | | | 49*|1 - -----------| 343*|1 - -----------| | \ \ 7 / \ 7 / /
$$4 \left(\frac{60 \left(x - 1\right)^{3}}{\left(- 4 \left(x - 1\right)^{2} + 7\right)^{\frac{5}{2}}} + \frac{48 \sqrt{7} \left(x - 1\right)^{2}}{343 \left(- \frac{4}{7} \left(x - 1\right)^{2} + 1\right)^{\frac{5}{2}}} + \frac{15 x - 15}{\left(- 4 \left(x - 1\right)^{2} + 7\right)^{\frac{3}{2}}} + \frac{4 \sqrt{7}}{49 \left(- \frac{4}{7} \left(x - 1\right)^{2} + 1\right)^{\frac{3}{2}}}\right)$$