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

解答

导数

\frac{x ^{2}}{x + 1}

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

求解步骤

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

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

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

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

化简

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

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

\frac{d}{d y} (cos (x) sin (y))

d er i v a t i v e \frac{3}{sin ( x ) + cos ( x )}

i = 1 \sum \infty i^{4}

\frac{\partial}{\partial x} (3 x^{4} + 8 x^{3})

\frac{d}{d z} ((1 - y) z)