(\partial)/(\partial x)((sin(x))/(sqrt(x)))

解答

\frac{\partial}{\partial x} (\frac{sin ( x )}{x})

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

求解步骤

\frac{\partial}{\partial x} (\frac{sin ( x )}{x})

使用微分除法定则:

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

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

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

\frac{\partial}{\partial x} (x) = \frac{1}{2 x}

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

化简

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

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

\int p cos (\frac{π x}{2 l}) d x

x \to 1 - lim (\frac{3}{∣ x - 1 ∣})

\frac{\partial}{\partial x} (3 x^{\frac{1}{2}})

\int \frac{1}{( 9 + x ^{2} ) ^{3}} d x

\int \frac{e}{x} d x