derivative of x/(7+x^2)

解答

\frac{d}{d x} (\frac{x}{7 + x ^{2}})

\frac{7 - x ^{2}}{( 7 + x ^{2} ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{x}{7 + 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 x}{d x} ( 7 + x ^{2} ) - \frac{d}{d x} ( 7 + x ^{2} ) x}{( 7 + x ^{2} ) ^{2}}

\frac{d x}{d x} = 1

\frac{d}{d x} (7 + x^{2}) = 2 x

= \frac{1 \cdot ( 7 + x ^{2} ) - 2 xx}{( 7 + x ^{2} ) ^{2}}

1 \cdot (7 + x^{2}) - 2 xx = 7 - x^{2}

= \frac{7 - x ^{2}}{( 7 + x ^{2} ) ^{2}}

\int (cot (x))^{2} d x

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

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

\int \frac{y}{( y + 2 ) ( 4 y - 1 )} d y

t an g e n t y = 4.5 x^{2} - 3 x + 2