derivative of (x^2-9/(sqrt(x-3)))

解答

\frac{d}{d x} (\frac{x ^{2} - 9}{x - 3})

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

求解步骤

\frac{d}{d x} (\frac{x ^{2} - 9}{x - 3})

化简

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

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

使用微分乘法定则:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x + 3, g = x - 3

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

\frac{d}{d x} (x + 3) = 1

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

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

化简

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

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

\frac{d}{d x} (e^{x} (- x^{\frac{2}{3}} - \frac{4}{3} x^{- \frac{3}{2}}))

\int x^{2} (x^{3} + 2)^{4} d x

\int_{0}^{1} x (1 - x)^{2} d x

x \to + (- 2) lim (x^{2} - x + 4)

y^{^{''}} - 6 y^{^{'}} + 9 y = 4 t e^{3 t}