derivative f(x)=(x^2)/((x^3)(x^2))

解答

导数

f (x) = \frac{x ^{2}}{( x ^{3} ) ( x ^{2} )}

- \frac{3}{x ^{4}}

求解步骤

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

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

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

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

化简

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

= - \frac{3}{x ^{4}}

\int \frac{1}{x x ^{2} - 81} d x

d er i v a t i v e f (t) = t^{4} - 20 t^{3} + 112 t^{2}

t an g e n t f (x) = arccos (x) + x, at x = 0

t \frac{d y}{d t} + 18 y = \frac{1}{t}

t an g e n t f (x) = \frac{2 x - 1}{x + 3}, at x = 3