derivative f(x)=(4x-5)/(sqrt(x))

解答

导数

f (x) = \frac{4 x - 5}{x}

\frac{4 x + 5}{2 x x}

求解步骤

\frac{d}{d x} (\frac{4 x - 5}{x})

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} ( 4 x - 5 ) x - \frac{d}{d x} ( x ) ( 4 x - 5 )}{( x ) ^{2}}

\frac{d}{d x} (4 x - 5) = 4

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

= \frac{4 x - \frac{1}{2 x} ( 4 x - 5 )}{( x ) ^{2}}

化简

\frac{4 x - \frac{1}{2 x} ( 4 x - 5 )}{( x ) ^{2}} : \frac{4 x + 5}{2 x x}

= \frac{4 x + 5}{2 x x}

a re a x^{2} + 10 x + 25, - 2 x - 2, - 5, - 1

\int (4 x + 8) sin (x^{2} + 4 x - 2) d x

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

\frac{d y}{d x} + 5 y - 20 = 0

n = 1 \sum \infty 7