derivative of (5x+2/(sqrt(x+1)))

解答

\frac{d}{d x} (\frac{5 x + 2}{x + 1})

\frac{5 x + 8}{2 ( x + 1 ) x + 1}

求解步骤

\frac{d}{d x} (\frac{5 x + 2}{x + 1})

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

\frac{d}{d x} (5 x + 2) = 5

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

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

化简

\frac{5 x + 1 - \frac{1}{2 x + 1} ( 5 x + 2 )}{( x + 1 ) ^{2}} : \frac{5 x + 8}{2 ( x + 1 ) x + 1}

= \frac{5 x + 8}{2 ( x + 1 ) x + 1}

in v erse l a pl a ce \frac{4}{s + 4}

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

x \to \infty lim ((1 + \frac{3}{x})^{\frac{x}{4}})

d er i v a t i v e h (x) = ln (x + x^{2} - 7)

in v erse l a pl a ce \frac{- 2 s + 1}{s ^{2} + 2 s - 8}