Question

Срочно!20 баллов! Решить производная y=cos x + tg x y=5sin 3 x y=4x5 + tg 3x - cos ²x

Answer 1

Y = cosx + tgx
y' = -sinx + 1/cos²x

y = 5sin3x
y ' = 5·3cos3x = 15cos3x

y = 4x⁵ + tg3x - cos²x 
y' = 4·5x⁴ + 3/cos²x + 2sinxcosx = 20x⁴ + sin2x + 3/cos²x

P.s.: u = cosx, v = u²
y' = u'v' = (cosx)'(u²)' = -sinx·2u = -sinx·2cosx = -2sinxcosx

(sinx)' = cosx
(cosx)' = -sinx
(tgx)' - 1/cos²x
(xⁿ)' = nxⁿ⁻¹

Answer 2

1) tg³x - tg²x - 4tgx + 4 = (tgx - 1)(tgx - 2)(tgx + 2) = 0
2) разделить на cos²x