а) y'= -2 - 6xПодставляем x0=1:y'(1) = -2 - 6*1 = -8
б) y' = sec^2x + 2cosxПодставляем x0=π/4:y'(π/4) = sec^2(π/4) + 2cos(π/4) = 2 + 2*sqrt(2)/2 = 2 + sqrt(2)
в) y' = sinx(2/x - 1)' + sinx'(2/x - 1) = sinx(-2/x^2) + sinx2x^(-2) = -2cosx/x + 2cosx/x = 0
г) y' = 3x^2 - 1/(sinx sin^2(x)) = 3x^2 - cosecxПодставляем x0=1:y'(1) = 31^2 - cosec(1) = 3 - 1/sin(1)
а) y'= -2 - 6x
Подставляем x0=1:
y'(1) = -2 - 6*1 = -8
б) y' = sec^2x + 2cosx
Подставляем x0=π/4:
y'(π/4) = sec^2(π/4) + 2cos(π/4) = 2 + 2*sqrt(2)/2 = 2 + sqrt(2)
в) y' = sinx(2/x - 1)' + sinx'(2/x - 1) = sinx(-2/x^2) + sinx2x^(-2) = -2cosx/x + 2cosx/x = 0
г) y' = 3x^2 - 1/(sinx sin^2(x)) = 3x^2 - cosecx
Подставляем x0=1:
y'(1) = 31^2 - cosec(1) = 3 - 1/sin(1)