а) y=x-x^3y' = 1 - 3x^2
б) y = √x + x^2/2y' = 1/(2√x) + 2x/2 = 1/(2√x) + x
в) y = x-1/x+1y' = 1 + 1/x^2
г) y = sin(3x)y' = 3cos(3x)
д) y=x tan(x/2)y' = tan(x/2) + xsec^2(x/2)/2
е) y = e^x cos(x)y' = e^x cos(x) - e^x * sin(x)
а) y=x-x^3
y' = 1 - 3x^2
б) y = √x + x^2/2
y' = 1/(2√x) + 2x/2 = 1/(2√x) + x
в) y = x-1/x+1
y' = 1 + 1/x^2
г) y = sin(3x)
y' = 3cos(3x)
д) y=x tan(x/2)
y' = tan(x/2) + xsec^2(x/2)/2
е) y = e^x cos(x)
y' = e^x cos(x) - e^x * sin(x)