derivative (sqrt(x)-3)/(sqrt(x)+3)

解答

导数

\frac{x - 3}{x + 3}

\frac{3}{x ( x + 3 ) ^{2}}

求解步骤

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

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

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

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

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

化简

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

= \frac{3}{x ( x + 3 ) ^{2}}

\int \frac{e ^{x}}{e ^{2 x} + 8 e ^{x} + 16} d x

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

\int 6 x + 4 d x

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

n = 4 \sum \infty \frac{1}{n ^{2} - 5 n + 6}