a) y=x^4 -3x^8 +9 y' = 4x^3 - 24x^7
б) y=1/x -16√x y' = -(1/(x^2)) - (8/sqrt(x))
в) y=-3/x -7tgx + x/8 y' = 3/(x^2) - 7/(cos^2(x)) + 1/8
г) y=cosx + 4√x y' = -sinx + 2/sqrt(x)
д) y= 2cosx + 4√x y' = -2sinx + 2/sqrt(x)
а) y=x *ctgx y' = ctgx - (x/(sin^2(x)))
б) y=√x *tgx y' = tgx/2*sqrt(x) + sqrt(x)/cos^2(x)
в) y=sinx/x y' = (cosx*x - sinx) / sin^2(x)
г) y=3x+3/3x-3 = y' = ( (3x+3)' * (3x-3) - (3x+3) * (3x-3)' ) / ((3x-3)^2) = (3(3x-3) - 3(3x+3))/ (3x-3)^2
а) y=(3x-4)^6 y' = 6(3x-4)^5 * 3 = 18(3x-4)^5
б) y=√7x-√3 y' = √7√x -√3 = (√7)/2x + 0 + 0 = (√7)/2x
в) y=sin(3x- π/4)
(c*f(x))' = c*f(x)' умножим потом на -1.
y' = (cos(3x + π/4))' = (cos(3x + π/4))'(3x+π/4)' = -3sin(3x+π/4)
Обратно умножим на -1
3sin(3x+π/4)