derivative of (x^2+3/(x^2+5))

解答

\frac{d}{d x} (\frac{x ^{2} + 3}{x ^{2} + 5})

\frac{4 x}{( x ^{2} + 5 ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{x ^{2} + 3}{x ^{2} + 5})

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 ^{2} + 5 ) - \frac{d}{d x} ( x ^{2} + 5 ) ( x ^{2} + 3 )}{( x ^{2} + 5 ) ^{2}}

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

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

= \frac{2 x ( x ^{2} + 5 ) - 2 x ( x ^{2} + 3 )}{( x ^{2} + 5 ) ^{2}}

乘开

2 x (x^{2} + 5) - 2 x (x^{2} + 3) : 4 x

= \frac{4 x}{( x ^{2} + 5 ) ^{2}}

\int cos^{3} (x s i) n^{2} x d x

\frac{\partial}{\partial x} (- 3 \cdot x^{2} + 28)

\int 2 e^{\frac{x}{2}} x^{3} d x

\frac{d}{d x} (\frac{3 - 5 x - x ^{2}}{x ^{2} - 6})

x \to 0 lim (\frac{x}{x ^{2} - 5 x})