derivative (9+2x-6sqrt(x))/x

解答

导数

\frac{9 + 2 x - 6 x}{x}

\frac{3 x - 9}{x ^{2}}

求解步骤

\frac{d}{d x} (\frac{9 + 2 x - 6 x}{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} ( 9 + 2 x - 6 x ) x - \frac{d x}{d x} ( 9 + 2 x - 6 x )}{x ^{2}}

\frac{d}{d x} (9 + 2 x - 6 x) = - \frac{3}{x} + 2

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

= \frac{( - \frac{3}{x} + 2 ) x - 1 \cdot ( 9 + 2 x - 6 x )}{x ^{2}}

化简

\frac{( - \frac{3}{x} + 2 ) x - 1 \cdot ( 9 + 2 x - 6 x )}{x ^{2}} : \frac{3 x - 9}{x ^{2}}

= \frac{3 x - 9}{x ^{2}}

y^{^{''}} + y^{^{'}} - 2 y = 0

\frac{d}{d x} (- x^{4} + 50 x^{2} - 300)

\int_{2}^{\infty} x e^{- 5 x} d x

x \to 0 + lim (tan (x^{2}) ln (x))

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