Tg³x + 2tg²x + 3tgx = 0
tgx(tg²x + 2tgx + 3) = 0
tgx = 0 tg²x + 2tgx + 3 = 0
x =πn, n ∈ z tgx = m
m² + 2m + 3 = 0
D = 2² - 4 * 3 = 4 - 12 = - 8 < 0 - решений нет
Ответ : πn , n ∈ z
1. (3x² - 1/x³) ' = (3x²) ' - (1/x³) ' = 6x - (x⁻³)' = 6x + 3x⁻⁴ = 6x + 3/x⁴
2. ((x/3 + 7)⁶) ' = 6(x/3 + 7)⁵ · (x/3 + 7)' = 6(x/3 + 7)⁵ · 1/3 = 2(x/3 +7)⁵
3. (eˣ·cosx) ' = (eˣ)' · cosx + eˣ · (cosx)' = eˣ · cosx + eˣ · (- sinx) = eˣ(cosx - sinx)
4. (2ˣ / sinx) ' =
![\frac{ (2^{x})'sinx - 2^{x}(sinx)' }{ sin^{2}x } = \frac{ 2^{x}ln2 sinx - 2^{x}cosx }{ sin^{2}x }](https://tex.z-dn.net/?f=+%5Cfrac%7B+%282%5E%7Bx%7D%29%27sinx+-++2%5E%7Bx%7D%28sinx%29%27++%7D%7B+sin%5E%7B2%7Dx+%7D+%3D++%5Cfrac%7B+2%5E%7Bx%7Dln2+sinx+-++2%5E%7Bx%7Dcosx++%7D%7B+sin%5E%7B2%7Dx+%7D+)
5. (2x³ - 1/x²)' = (2x³) ' - (x⁻²)' = 6x² + 2x⁻³ = 6x² + 2/x³
6. ((x/7 + 13)⁸) ' = 8(x/7 + 13)⁷ · (x/7 + 13)' = 8(x/7 + 13)⁷ · 1/7 = 8/7 (x/7 + 13)⁷
7. (eˣsinx) ' = (eˣ) ' sinx + eˣ (sinx) ' = eˣ sinx + eˣ cosx
8. (3ˣ / cosx) ' =
![\frac{ (3^{x})'cosx - 3^{x}(cosx)' }{ cos^{2}x } = \frac{ 3^{x} ln3 cosx + 3^{x} sinx }{ cos^{2}x }](https://tex.z-dn.net/?f=+%5Cfrac%7B+%283%5E%7Bx%7D%29%27cosx+-++3%5E%7Bx%7D%28cosx%29%27++%7D%7B+cos%5E%7B2%7Dx+%7D++%3D++%5Cfrac%7B+3%5E%7Bx%7D+ln3+cosx+%2B++3%5E%7Bx%7D+sinx++%7D%7B+cos%5E%7B2%7Dx+%7D+)
Линейная функция задается уравнением вида у=kx+b
а) у=х/3+4 - линейная k=1/3, b=4
б) у=3/х+4; в) у=-2х- линейная k=-2, b=0
г) у=4 - линейная k=0, b=4
д) у=-2/х.
Sin A = 4/5 = 0,8.
15 = a/ 2*0,8;
15 = a / 1,6;
a = 15 * 1,6;
a = 24