derivative of (x+4/(7x^2e^x))

解答

\frac{d}{d x} (\frac{x + 4}{7 x ^{2} e ^{x}})

- \frac{x ^{2} + 5 x + 8}{7 e ^{x} x ^{3}}

求解步骤

\frac{d}{d x} (\frac{x + 4}{7 x ^{2} e ^{x}})

将常数提出:

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

= \frac{1}{7} \frac{d}{d x} (\frac{x + 4}{x ^{2} e ^{x}})

使用微分除法定则:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{1}{7} \cdot \frac{\frac{d}{d x} ( x + 4 ) x ^{2} e ^{x} - \frac{d}{d x} ( x ^{2} e ^{x} ) ( x + 4 )}{( x ^{2} e ^{x} ) ^{2}}

\frac{d}{d x} (x + 4) = 1

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

= \frac{1}{7} \cdot \frac{1 \cdot x ^{2} e ^{x} - ( 2 x e ^{x} + e ^{x} x ^{2} ) ( x + 4 )}{( x ^{2} e ^{x} ) ^{2}}

化简

\frac{1}{7} \cdot \frac{1 \cdot x ^{2} e ^{x} - ( 2 x e ^{x} + e ^{x} x ^{2} ) ( x + 4 )}{( x ^{2} e ^{x} ) ^{2}} : - \frac{x ^{2} + 5 x + 8}{7 e ^{x} x ^{3}}

= - \frac{x ^{2} + 5 x + 8}{7 e ^{x} x ^{3}}

\int \frac{( 4 + 10 x )}{7 + 4 x + 5 x ^{2}} d x

y^{^{'}} + 3 y = e^{- 2 x}

\int_{- 3}^{4} ((y + 12) - (y^{2})) d y

y^{^{''}} + 7 y^{^{'}} + 6 y = 0

d er i v a t i v e f (x) = 2 (x)^{3} ln (x)