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

解答

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

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

求解步骤

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

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

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

\frac{d x}{d x} = 1

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

化简

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

d er i v a t i v e \frac{1}{3} x^{3} + 8 x^{2} + 63 x + 7

y^{^{''}} x + (\frac{2}{x} - \frac{2 x}{1 + x ^{2}}) \cdot y^{^{'}} = 0

\frac{d}{d x} (2 cos (x) - 4 sin (x))

\int 2 arcsin (2 x) d x

\int \frac{1}{169 - 16 x ^{2}} d x