derivative g(x)=(2x-sqrt(x))(5x+2)

解答

导数

g (x) = (2 x - x) (5 x + 2)

\frac{- 15 x + 40 x x - 2}{2 x} + 4

求解步骤

\frac{d}{d x} ((2 x - x) (5 x + 2))

使用微分乘法定则:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 2 x - x, g = 5 x + 2

= \frac{d}{d x} (2 x - x) (5 x + 2) + \frac{d}{d x} (5 x + 2) (2 x - x)

\frac{d}{d x} (2 x - x) = 2 - \frac{1}{2 x}

\frac{d}{d x} (5 x + 2) = 5

= (2 - \frac{1}{2 x}) (5 x + 2) + 5 (2 x - x)

化简

(2 - \frac{1}{2 x}) (5 x + 2) + 5 (2 x - x) : \frac{- 15 x + 40 x x - 2}{2 x} + 4

= \frac{- 15 x + 40 x x - 2}{2 x} + 4

\frac{d y}{d t} = t^{2} (1 + 15 y)

\frac{\partial}{\partial x} (x^{2} sin (3 x - 2 y))

x \to a lim (g (x))

y^{^{''}} + y = t

y^{^{''}} - 4 y^{^{'}} - 5 y = 9 e^{2} t