derivative of x/((5x-4^3))

解答

\frac{d}{d x} (\frac{x}{( 5 x - 4 ) ^{3}})

- \frac{2 ( 5 x + 2 )}{( 5 x - 4 ) ^{4}}

求解步骤

\frac{d}{d x} (\frac{x}{( 5 x - 4 ) ^{3}})

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} ( 5 x - 4 ) ^{3} - \frac{d}{d x} ( ( 5 x - 4 ) ^{3} ) x}{( ( 5 x - 4 ) ^{3} ) ^{2}}

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

\frac{d}{d x} ((5 x - 4)^{3}) = 15 (5 x - 4)^{2}

= \frac{1 \cdot ( 5 x - 4 ) ^{3} - 15 ( 5 x - 4 ) ^{2} x}{( ( 5 x - 4 ) ^{3} ) ^{2}}

化简

\frac{1 \cdot ( 5 x - 4 ) ^{3} - 15 ( 5 x - 4 ) ^{2} x}{( ( 5 x - 4 ) ^{3} ) ^{2}} : - \frac{2 ( 5 x + 2 )}{( 5 x - 4 ) ^{4}}

= - \frac{2 ( 5 x + 2 )}{( 5 x - 4 ) ^{4}}

t \to 0 lim (\frac{( 2 e ^{t} - 2 )}{t})

d er i v a t i v e e^{x} x

x \to 0 + lim (x^{2} sin (\frac{1}{x}))

\frac{\partial}{\partial y} (4 y^{3} - 100 y)

\int_{1}^{3} 2 4 x^{3} d x