derivative (xf(x))/5

解答

导数

\frac{x f ( x )}{5}

\frac{2 x f}{5}

求解步骤

\frac{d}{d x} (\frac{x f x}{5})

将

f

视为常数

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{f}{5} \frac{d}{d x} (xx)

使用微分乘法定则:

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

f = x, g = x

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

\frac{d x}{d x} = 1

\frac{d x}{d x} = 1

= \frac{f}{5} (1 \cdot x + 1 \cdot x)

化简

\frac{f}{5} (1 \cdot x + 1 \cdot x) : \frac{2 x f}{5}

= \frac{2 x f}{5}

\int \frac{( 5 x + 3 )}{( x ^{2} - 9 )} d x

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

\int_{- 1}^{1} (1 + 1 - x^{2}) d x

t^{2} y^{^{''}} + 19 t y^{^{'}} + 162 y = 0

d er i v a t i v e 3 cos (2 u)