derivative of-(x^3+8x^2+19x+12/((x+20)))

解答

\frac{d}{d x} (- \frac{x ^{3} + 8 x ^{2} + 19 x + 12}{( x + 20 )})

- \frac{2 x ^{3} + 68 x ^{2} + 320 x + 368}{( x + 20 ) ^{2}}

求解步骤

\frac{d}{d x} (- \frac{x ^{3} + 8 x ^{2} + 19 x + 12}{( x + 20 )})

将常数提出:

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

= - \frac{d}{d x} (\frac{x ^{3} + 8 x ^{2} + 19 x + 12}{x + 20})

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 ^{3} + 8 x ^{2} + 19 x + 12 ) ( x + 20 ) - \frac{d}{d x} ( x + 20 ) ( x ^{3} + 8 x ^{2} + 19 x + 12 )}{( x + 20 ) ^{2}}

\frac{d}{d x} (x^{3} + 8 x^{2} + 19 x + 12) = 3 x^{2} + 16 x + 19

\frac{d}{d x} (x + 20) = 1

= - \frac{( 3 x ^{2} + 16 x + 19 ) ( x + 20 ) - 1 \cdot ( x ^{3} + 8 x ^{2} + 19 x + 12 )}{( x + 20 ) ^{2}}

化简

- \frac{( 3 x ^{2} + 16 x + 19 ) ( x + 20 ) - 1 \cdot ( x ^{3} + 8 x ^{2} + 19 x + 12 )}{( x + 20 ) ^{2}} : - \frac{2 x ^{3} + 68 x ^{2} + 320 x + 368}{( x + 20 ) ^{2}}

= - \frac{2 x ^{3} + 68 x ^{2} + 320 x + 368}{( x + 20 ) ^{2}}

\frac{d}{d x} (a \cdot x + b)

\int \frac{4 x - 5}{4 x ^{2} - 12 x + 13} d x

\int \frac{e ^{- l n (1 - x^{2})}}{x ^{2}} d x

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

d er i v a t i v e \frac{2 x ^{2} + 6 x + 6}{x}