derivative of (-cos(x)/(4x^2+2x-3))

解答

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

- \frac{- sin ( x ) ( 4 x ^{2} + 2 x - 3 ) - cos ( x ) ( 8 x + 2 )}{( 4 x ^{2} + 2 x - 3 ) ^{2}}

求解步骤

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

化简

\frac{- cos ( x )}{4 x ^{2} + 2 x - 3} : - \frac{cos ( x )}{4 x ^{2} + 2 x - 3}

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

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

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

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

\frac{d}{d x} (cos (x)) = - sin (x)

\frac{d}{d x} (4 x^{2} + 2 x - 3) = 8 x + 2

= - \frac{( - sin ( x ) ) ( 4 x ^{2} + 2 x - 3 ) - ( 8 x + 2 ) cos ( x )}{( 4 x ^{2} + 2 x - 3 ) ^{2}}

化简

= - \frac{- sin ( x ) ( 4 x ^{2} + 2 x - 3 ) - cos ( x ) ( 8 x + 2 )}{( 4 x ^{2} + 2 x - 3 ) ^{2}}

\frac{d y}{d t} + 2 y = 3 t^{2} + 2 t - 1

n = 1 \sum \infty \frac{8 ^{n}}{n ^{4}}

(x + 1) \frac{d y}{d x} + (x + 2) y = 4 x e^{- x}

\int \frac{x}{16 - x ^{4}} d x

\frac{\partial}{\partial x} (x - x y + 3)