derivative of x/(4-sqrt(16-x^2))

解答

\frac{d}{d x} (\frac{x}{4 - 16 - x ^{2}})

\frac{4}{( - x ^{2} + 16 - 4 ) - x ^{2} + 16}

求解步骤

\frac{d}{d x} (\frac{x}{4 - 16 - 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} ( 4 - 16 - x ^{2} ) - \frac{d}{d x} ( 4 - 16 - x ^{2} ) x}{( 4 - 16 - x ^{2} ) ^{2}}

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

\frac{d}{d x} (4 - 16 - x^{2}) = \frac{x}{- x ^{2} + 16}

= \frac{1 \cdot ( 4 - 16 - x ^{2} ) - \frac{x}{- x ^{2} + 16} x}{( 4 - 16 - x ^{2} ) ^{2}}

化简

\frac{1 \cdot ( 4 - 16 - x ^{2} ) - \frac{x}{- x ^{2} + 16} x}{( 4 - 16 - x ^{2} ) ^{2}} : \frac{4}{( - x ^{2} + 16 - 4 ) - x ^{2} + 16}

= \frac{4}{( - x ^{2} + 16 - 4 ) - x ^{2} + 16}

t an g e n t f (x) = 5 - 2 x^{2}, (- 5, - 45)

\int_{0}^{2} (1 + x)^{\frac{1}{3}} \cdot 2 d x

x y^{'} + (1 + x \cdot cot (x)) y = 0

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

a re a y = 3 - x^{2}, y = 11 - 6 x