Question

Найдите производную функции

Answer 1

в) y = (x^2 + 3)(x^4 - 1)
y' = 2x(x^4 - 1) + 4x^3(x^2 + 3)
г) y = (x^2 - 2)(x^7 + 4)
y' = 2x(x^7 + 4) + 7x^6(x^2 - 2)
в) y = √x*(8x - 10)
y' = 1/(2√x)*(8x - 10) + 8√x
г)  y = √x*(x^4 + 2)
y' = 1/(2√x)*(x^4 + 2) + √x*4x^3
в)  y = x*cos x
y' = cos x + x(-sin x) = cos x - x*sin x
г)  y = √x*sin x
y' = 1/(2√x)*sin x + √x*cos x
в) y = (1/x + 8)(5x - 2) = 5 + 40x - 2/x - 16
y' = 40 + 2/x^2
г) y = (9 - 1/x)(3x + 2) = 27x - 3 + 18 - 2/x
y' = 27 + 2/x^2
в) y = 1/x*ctg x
y' = -1/x^2*ctg x - 1/x*1/sin^2 x
г) y = sin x*tg x
y' = cos x*tg x + sin x/cos^2 x = sin x + sin x/cos^2 x