derivative of x/(sqrt(x-4))

解答

\frac{d}{d x} (\frac{x}{x - 4})

\frac{x - 8}{2 ( x - 4 ) x - 4}

求解步骤

\frac{d}{d x} (\frac{x}{x - 4})

使用微分除法定则:

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

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

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

\frac{d}{d x} (x - 4) = \frac{1}{2 x - 4}

= \frac{1 \cdot x - 4 - \frac{1}{2 x - 4} x}{( x - 4 ) ^{2}}

化简

\frac{1 \cdot x - 4 - \frac{1}{2 x - 4} x}{( x - 4 ) ^{2}} : \frac{x - 8}{2 ( x - 4 ) x - 4}

= \frac{x - 8}{2 ( x - 4 ) x - 4}

\int \frac{x ^{3}}{2 x ^{4} + 1} d x

x \to 5 lim (4 x - 5)

\int \frac{21 π}{2} cos (\frac{21 π x}{2}) d x

\frac{d}{d x} (\frac{2 cos ( x )}{1 + sin ( x )})

x \to \infty lim (x^{2} - x)