derivative of (x-19/(sqrt(x)-\sqrt{19)})

解答

\frac{d}{d x} (\frac{x - 19}{x - 19})

\frac{x - 2 19 x + 19}{2 x ( x - 19 ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{x - 19}{x - 19})

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} ( x - 19 ) ( x - 19 ) - \frac{d}{d x} ( x - 19 ) ( x - 19 )}{( x - 19 ) ^{2}}

\frac{d}{d x} (x - 19) = 1

\frac{d}{d x} (x - 19) = \frac{1}{2 x}

= \frac{1 \cdot ( x - 19 ) - \frac{1}{2 x} ( x - 19 )}{( x - 19 ) ^{2}}

化简

\frac{1 \cdot ( x - 19 ) - \frac{1}{2 x} ( x - 19 )}{( x - 19 ) ^{2}} : \frac{x - 2 19 x + 19}{2 x ( x - 19 ) ^{2}}

= \frac{x - 2 19 x + 19}{2 x ( x - 19 ) ^{2}}

t an g e n t f (x) = x^{4} - 13 x^{2} + 36, at x = 1

l a pl a ce t r an s f or m (25 t) ((\frac{t}{25})^{2})

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

n = 0 \sum \infty \frac{1}{2 ( 2 ) ^{n}}

\int tan^{2} (6 t) d t