derivative of x/((2x-1^6))

解答

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

\frac{- 1 - 10 x}{( 2 x - 1 ) ^{7}}

求解步骤

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

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

\frac{d}{d x} ((2 x - 1)^{6}) = 12 (2 x - 1)^{5}

= \frac{1 \cdot ( 2 x - 1 ) ^{6} - 12 ( 2 x - 1 ) ^{5} x}{( ( 2 x - 1 ) ^{6} ) ^{2}}

化简

\frac{1 \cdot ( 2 x - 1 ) ^{6} - 12 ( 2 x - 1 ) ^{5} x}{( ( 2 x - 1 ) ^{6} ) ^{2}} : \frac{- 1 - 10 x}{( 2 x - 1 ) ^{7}}

= \frac{- 1 - 10 x}{( 2 x - 1 ) ^{7}}

\int (4 x + 3)^{3} d x

f (x) = e^{x^{2}} \cdot 2 x

\int 5 x^{3} 1 - x^{2} d x

\frac{\partial}{\partial x} (2 x^{2} - 4 x y + x yz)

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