derivative of (x-13/(sqrt(x)-\sqrt{13)})

解答

\frac{d}{d x} (\frac{x - 13}{x - 13})

\frac{x - 2 13 x + 13}{2 x ( x - 13 ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{x - 13}{x - 13})

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 - 13 ) ( x - 13 ) - \frac{d}{d x} ( x - 13 ) ( x - 13 )}{( x - 13 ) ^{2}}

\frac{d}{d x} (x - 13) = 1

\frac{d}{d x} (x - 13) = \frac{1}{2 x}

= \frac{1 \cdot ( x - 13 ) - \frac{1}{2 x} ( x - 13 )}{( x - 13 ) ^{2}}

化简

\frac{1 \cdot ( x - 13 ) - \frac{1}{2 x} ( x - 13 )}{( x - 13 ) ^{2}} : \frac{x - 2 13 x + 13}{2 x ( x - 13 ) ^{2}}

= \frac{x - 2 13 x + 13}{2 x ( x - 13 ) ^{2}}

s l o p e (1.2) (- 2.14)

\frac{d}{d x} (\frac{sinh ( x )}{cosh ( x )})

\frac{d}{d x} (\frac{x - 10}{x - 10})

x \to \infty lim (2 + \frac{3}{x})

\int 12 x^{2} 1 - x^{2} d x