derivative ((1-ln(x)))/(11x^2)

解答

导数

\frac{( 1 - ln ( x ) )}{11 x ^{2}}

- \frac{- 2 ln ( x ) + 3}{11 x ^{3}}

求解步骤

\frac{d}{d x} (\frac{1 - ln ( x )}{11 x ^{2}})

将常数提出:

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

= \frac{1}{11} \frac{d}{d x} (\frac{1 - ln ( x )}{x ^{2}})

使用微分除法定则:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{1}{11} \cdot \frac{\frac{d}{d x} ( 1 - ln ( x ) ) x ^{2} - \frac{d}{d x} ( x ^{2} ) ( 1 - ln ( x ) )}{( x ^{2} ) ^{2}}

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

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

= \frac{1}{11} \cdot \frac{( - \frac{1}{x} ) x ^{2} - 2 x ( 1 - ln ( x ) )}{( x ^{2} ) ^{2}}

化简

\frac{1}{11} \cdot \frac{( - \frac{1}{x} ) x ^{2} - 2 x ( 1 - ln ( x ) )}{( x ^{2} ) ^{2}} : - \frac{- 2 ln ( x ) + 3}{11 x ^{3}}

= - \frac{- 2 ln ( x ) + 3}{11 x ^{3}}

\int_{- 1}^{3} ∣ x ∣ d x

\int \frac{6 x + 6}{x ^{2} + 2 x - 3} d x

\int 2 x y cos (x y^{2}) d y

\frac{d}{d x} (a r (x) c, x)

y^{^{''}} - 8 y + 16 = 0