derivative (x^2+6)/(5x-2)

解答

导数

\frac{x ^{2} + 6}{5 x - 2}

\frac{5 x ^{2} - 4 x - 30}{( 5 x - 2 ) ^{2}}

求解步骤

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

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

\frac{d}{d x} (x^{2} + 6) = 2 x

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

= \frac{2 x ( 5 x - 2 ) - 5 ( x ^{2} + 6 )}{( 5 x - 2 ) ^{2}}

乘开

2 x (5 x - 2) - 5 (x^{2} + 6) : 5 x^{2} - 4 x - 30

= \frac{5 x ^{2} - 4 x - 30}{( 5 x - 2 ) ^{2}}

\int e^{(y^{2})} d y

\int_{0}^{1} (x - x) d x

\frac{\partial}{\partial x} (y - \frac{1}{x ^{2}})

d er i v a t i v e e^{(\frac{1}{t} l n (\frac{5 ^{t} + 1 3 ^{t}}{2}))}

\frac{d y}{d t} + 50 y = 0