derivative f(x)= x/((x^2+15x+50))

解答

导数

f (x) = \frac{x}{( x ^{2} + 15 x + 50 )}

\frac{- x ^{2} + 50}{( x ^{2} + 15 x + 50 ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{x}{x ^{2} + 15 x + 50})

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} ( x ^{2} + 15 x + 50 ) - \frac{d}{d x} ( x ^{2} + 15 x + 50 ) x}{( x ^{2} + 15 x + 50 ) ^{2}}

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

\frac{d}{d x} (x^{2} + 15 x + 50) = 2 x + 15

= \frac{1 \cdot ( x ^{2} + 15 x + 50 ) - ( 2 x + 15 ) x}{( x ^{2} + 15 x + 50 ) ^{2}}

化简

\frac{1 \cdot ( x ^{2} + 15 x + 50 ) - ( 2 x + 15 ) x}{( x ^{2} + 15 x + 50 ) ^{2}} : \frac{- x ^{2} + 50}{( x ^{2} + 15 x + 50 ) ^{2}}

= \frac{- x ^{2} + 50}{( x ^{2} + 15 x + 50 ) ^{2}}

a re a 1 - x, y = 2, - 1, 1

\frac{d}{d x} (x^{2} 3 - 4 x)

\frac{\partial}{\partial y} (3 x e^{2 x y})

\frac{d}{d x} ((3 - 2 x^{2})^{2} 2 x^{2} + 1)

d er i v a t i v e \frac{x}{x - 4}