derivative (sqrt(x))(3-x)^2

解答

导数

(x) (3 - x)^{2}

\frac{5 x ^{2} - 18 x + 9}{2 x}

求解步骤

\frac{d}{d x} (x (3 - x)^{2})

使用微分乘法定则:

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

f = x, g = (3 - x)^{2}

= \frac{d}{d x} (x) (3 - x)^{2} + \frac{d}{d x} ((3 - x)^{2}) x

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

\frac{d}{d x} ((3 - x)^{2}) = - 2 (3 - x)

= \frac{1}{2 x} (3 - x)^{2} + (- 2 (3 - x)) x

化简

\frac{1}{2 x} (3 - x)^{2} + (- 2 (3 - x)) x : \frac{5 x ^{2} - 18 x + 9}{2 x}

= \frac{5 x ^{2} - 18 x + 9}{2 x}

\frac{d}{d x} (y cos (x ln (y)))

s im pl i f y \frac{x}{2 - x}

\frac{d y}{d x} = 5 (1 - \frac{x}{10})

\int_{- 2}^{0} - x + 2 d x

\int - 20 x^{- 5} d x