derivative of (sin(x)/(x^5))

解答

\frac{d}{d x} (\frac{sin ( x )}{x ^{5}})

\frac{x cos ( x ) - 5 sin ( x )}{x ^{6}}

求解步骤

\frac{d}{d x} (\frac{sin ( x )}{x ^{5}})

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

\frac{d}{d x} (sin (x)) = cos (x)

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

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

化简

\frac{cos ( x ) x ^{5} - 5 x ^{4} sin ( x )}{( x ^{5} ) ^{2}} : \frac{x cos ( x ) - 5 sin ( x )}{x ^{6}}

= \frac{x cos ( x ) - 5 sin ( x )}{x ^{6}}

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

t an g e n t y = (x^{3} - 9 x)^{10}, (3, 0)

t an g e n t y = 3 x^{3} - 3 x, (- 4, 0)

\int_{0}^{3} (5 - \frac{5}{3} x)^{2} d x

s l o p e (- 10.6) (- 5.8)