derivative ((x^2+3))/((x+1))

解答

导数

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

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

求解步骤

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

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

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

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

化简

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

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

d er i v a t i v e 2 tan (x) + sec (x) - 3 cot (x)

d er i v a t i v e \frac{x ^{3}}{3 - 3 x}

d er i v a t i v e 3^{x} + 2

d er i v a t i v e lo g_{10} (\frac{2}{x})

d er i v a t i v e \frac{( 3 x ^{2} - 1 ) ^{2}}{( x + 1 ) ^{3}}