derivative f(x)= x/(1-ln(x-6))

解答

导数

f (x) = \frac{x}{1 - ln ( x - 6 )}

\frac{2 x - ln ( x - 6 ) ( x - 6 ) - 6}{( x - 6 ) ( 1 - ln ( x - 6 ) ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{x}{1 - ln ( x - 6 )})

使用微分除法定则:

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

= \frac{\frac{d x}{d x} ( 1 - ln ( x - 6 ) ) - \frac{d}{d x} ( 1 - ln ( x - 6 ) ) x}{( 1 - ln ( x - 6 ) ) ^{2}}

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

\frac{d}{d x} (1 - ln (x - 6)) = - \frac{1}{x - 6}

= \frac{1 \cdot ( 1 - ln ( x - 6 ) ) - ( - \frac{1}{x - 6} ) x}{( 1 - ln ( x - 6 ) ) ^{2}}

化简

\frac{1 \cdot ( 1 - ln ( x - 6 ) ) - ( - \frac{1}{x - 6} ) x}{( 1 - ln ( x - 6 ) ) ^{2}} : \frac{2 x - ln ( x - 6 ) ( x - 6 ) - 6}{( x - 6 ) ( 1 - ln ( x - 6 ) ) ^{2}}

= \frac{2 x - ln ( x - 6 ) ( x - 6 ) - 6}{( x - 6 ) ( 1 - ln ( x - 6 ) ) ^{2}}

2 x + 2 y \frac{d y}{d x} = 0

\int_{0}^{5 r} 2 (25 r^{2} - y^{2}) d y

\int \frac{1}{y ^{3} + 1} d y

\int \frac{10 x ^{2} - 9 x + 20}{x ^{3} + 4 x} d x

x y^{^{'}} + x y - y^{^{'}} - 2 y = 0