derivative f(x)=(e^{x-3})/(x-2)

解答

导数

f (x) = \frac{e ^{x - 3}}{x - 2}

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

求解步骤

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

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

\frac{d}{d x} (e^{x - 3}) = e^{x - 3}

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

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

化简

\frac{e ^{x - 3} ( x - 2 ) - 1 \cdot e ^{x - 3}}{( x - 2 ) ^{2}} : \frac{e ^{x - 3} x - 3 e ^{x - 3}}{( x - 2 ) ^{2}}

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

\int_{1}^{7} \frac{1}{9 + ( x + 2 ) ^{2}} d x

\int (2 x^{3} - 3 x + 5) d x

\int x cot (x^{2}) d x

y^{^{'}} + y = e^{- t}

n = 1 \sum \infty \frac{n - 5}{n} + 5