derivative of x/(sqrt(x-6))

解答

\frac{d}{d x} (\frac{x}{x - 6})

\frac{x - 12}{2 ( x - 6 ) x - 6}

求解步骤

\frac{d}{d x} (\frac{x}{x - 6})

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 - 6 - \frac{d}{d x} ( x - 6 ) x}{( x - 6 ) ^{2}}

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

\frac{d}{d x} (x - 6) = \frac{1}{2 x - 6}

= \frac{1 \cdot x - 6 - \frac{1}{2 x - 6} x}{( x - 6 ) ^{2}}

化简

\frac{1 \cdot x - 6 - \frac{1}{2 x - 6} x}{( x - 6 ) ^{2}} : \frac{x - 12}{2 ( x - 6 ) x - 6}

= \frac{x - 12}{2 ( x - 6 ) x - 6}

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

l a pl a ce t r an s f or m 6 e^{- 5 t} + 5 t

d er i v a t i v e y = \frac{3 x ^{4} + 9}{x ^{2}}

\int (ln (x + 1))^{2} d x

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