derivative ((x^2))/(x^2+27)

解答

导数

\frac{( x ^{2} )}{x ^{2} + 27}

\frac{54 x}{( x ^{2} + 27 ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{x ^{2}}{x ^{2} + 27})

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} ( x ^{2} ) ( x ^{2} + 27 ) - \frac{d}{d x} ( x ^{2} + 27 ) x ^{2}}{( x ^{2} + 27 ) ^{2}}

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

\frac{d}{d x} (x^{2} + 27) = 2 x

= \frac{2 x ( x ^{2} + 27 ) - 2 x x ^{2}}{( x ^{2} + 27 ) ^{2}}

化简

\frac{2 x ( x ^{2} + 27 ) - 2 x x ^{2}}{( x ^{2} + 27 ) ^{2}} : \frac{54 x}{( x ^{2} + 27 ) ^{2}}

= \frac{54 x}{( x ^{2} + 27 ) ^{2}}

\frac{d}{d x} (\frac{cos ( x )}{lo g _{3} ( x )})

\int \frac{x}{4 x ^{2} + 5} d x

\frac{\partial}{\partial x} (\frac{r x ( K ( r , x ) - x )}{K ( r , x ) + a x})

f (x) = 3 x^{2} + 1

y^{^{'}} = \frac{( 4 t + y )}{4 y - t}