derivative (2x^3-7)/(x^2)

解答

导数

\frac{2 x ^{3} - 7}{x ^{2}}

\frac{2 ( x ^{3} + 7 )}{x ^{3}}

求解步骤

\frac{d}{d x} (\frac{2 x ^{3} - 7}{x ^{2}})

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} ( 2 x ^{3} - 7 ) x ^{2} - \frac{d}{d x} ( x ^{2} ) ( 2 x ^{3} - 7 )}{( x ^{2} ) ^{2}}

\frac{d}{d x} (2 x^{3} - 7) = 6 x^{2}

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

= \frac{6 x ^{2} x ^{2} - 2 x ( 2 x ^{3} - 7 )}{( x ^{2} ) ^{2}}

化简

\frac{6 x ^{2} x ^{2} - 2 x ( 2 x ^{3} - 7 )}{( x ^{2} ) ^{2}} : \frac{2 ( x ^{3} + 7 )}{x ^{3}}

= \frac{2 ( x ^{3} + 7 )}{x ^{3}}

x y^{^{'}} = y - x

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

\frac{d}{d x} (\frac{6}{x ^{2} - 9})

t an g e n t f (x) = 7 x + 4, at x = 3

\frac{d}{d x} (\frac{x ^{5} + 9}{x ^{3}})