derivative (sin(x)-x)/(x^2)

解答

导数

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

\frac{x + x cos ( x ) - 2 sin ( x )}{x ^{3}}

求解步骤

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

\frac{d}{d x} (sin (x) - x) = cos (x) - 1

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

= \frac{( cos ( x ) - 1 ) x ^{2} - 2 x ( sin ( x ) - x )}{( x ^{2} ) ^{2}}

化简

\frac{( cos ( x ) - 1 ) x ^{2} - 2 x ( sin ( x ) - x )}{( x ^{2} ) ^{2}} : \frac{x + x cos ( x ) - 2 sin ( x )}{x ^{3}}

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

(- 2 x y 2 - 1 y) d x + (- 2 x 2 y + 1 x) d y = 0

\frac{d}{d x} (e^{2 x} (2 x - 1))

d er i v a t i v e f (x) = 9 ln (9 + 2 x^{2})

\int cos^{6} (θ) d θ

t an g e n t f (x) = (x - x^{3}), at x = 1