derivative f(x)=(e^x)/(4x+1)

解答

导数

f (x) = \frac{e ^{x}}{4 x + 1}

\frac{4 e ^{x} x - 3 e ^{x}}{( 4 x + 1 ) ^{2}}

求解步骤

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

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

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

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

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

乘开

e^{x} (4 x + 1) - 4 e^{x} : 4 e^{x} x - 3 e^{x}

= \frac{4 e ^{x} x - 3 e ^{x}}{( 4 x + 1 ) ^{2}}

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

t an g e n t y = \frac{2 x}{x + 1}, (1, 1)

\frac{d}{d x} (\frac{5 x}{x + 1})

x \to + (- 1) lim (\frac{sin ( x )}{x})

\frac{d y}{d x} = y^{3}