derivative of x/((2x+3^3))

解答

\frac{d}{d x} (\frac{x}{( 2 x + 3 ) ^{3}})

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

求解步骤

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

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

\frac{d}{d x} ((2 x + 3)^{3}) = 6 (2 x + 3)^{2}

= \frac{1 \cdot ( 2 x + 3 ) ^{3} - 6 ( 2 x + 3 ) ^{2} x}{( ( 2 x + 3 ) ^{3} ) ^{2}}

化简

\frac{1 \cdot ( 2 x + 3 ) ^{3} - 6 ( 2 x + 3 ) ^{2} x}{( ( 2 x + 3 ) ^{3} ) ^{2}} : \frac{3 - 4 x}{( 2 x + 3 ) ^{4}}

= \frac{3 - 4 x}{( 2 x + 3 ) ^{4}}

\int x^{2} 8 + x^{3} d x

\frac{d}{d x} (5 x + \frac{2}{x})

x \to - 3 lim (x^{4} + 3 x + 9)

\int \frac{x + 4}{x ^{2} + 16} d x

y^{^{''}} - 5 y^{^{'}} + 6 y = e^{t}