derivative of (5-3x/(x^2+3x))

解答

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

\frac{3 x ^{2} - 10 x - 15}{( x ^{2} + 3 x ) ^{2}}

求解步骤

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

使用微分除法定则:

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

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

\frac{d}{d x} (5 - 3 x) = - 3

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

= \frac{( - 3 ) ( x ^{2} + 3 x ) - ( 2 x + 3 ) ( 5 - 3 x )}{( x ^{2} + 3 x ) ^{2}}

化简

\frac{( - 3 ) ( x ^{2} + 3 x ) - ( 2 x + 3 ) ( 5 - 3 x )}{( x ^{2} + 3 x ) ^{2}} : \frac{3 x ^{2} - 10 x - 15}{( x ^{2} + 3 x ) ^{2}}

= \frac{3 x ^{2} - 10 x - 15}{( x ^{2} + 3 x ) ^{2}}

t an g e n t cos (\frac{π x}{2})

\int_{0}^{1} 4 x arccos (x) d x

\int \frac{13 x ^{3}}{2 + x ^{2}} d x

d er i v a t i v e sin ((π x)^{3})

x^{2} y^{^{'}} - 2 x y = 5 y^{4}, y (1) = \frac{1}{4}