derivative of (sin(x)/(3x^2))

解答

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

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

求解步骤

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

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{3} \frac{d}{d x} (\frac{sin ( x )}{x ^{2}})

使用微分除法定则:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{1}{3} \cdot \frac{\frac{d}{d x} ( sin ( x ) ) x ^{2} - \frac{d}{d x} ( x ^{2} ) sin ( x )}{( x ^{2} ) ^{2}}

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

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

= \frac{1}{3} \cdot \frac{cos ( x ) x ^{2} - 2 x sin ( x )}{( x ^{2} ) ^{2}}

化简

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

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

x \to 3 lim (g (x))

d er i v a t i v e g (x) = (x - 4)^{3} + 3 x (x - 4)^{2}

\frac{\partial}{\partial x} (x y e^{- 9 y})

in v erse l a pl a ce \frac{a}{s}

\int_{2}^{6} 7 x^{3} d x