derivative of e^x 1/x

解答

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

\frac{e ^{x}}{x} - \frac{e ^{x}}{x ^{2}}

求解步骤

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

使用微分乘法定则:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{x}, g = \frac{1}{x}

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

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

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

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

化简

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

= \frac{e ^{x}}{x} - \frac{e ^{x}}{x ^{2}}

\frac{\partial}{\partial x} (ln (2 x + 1))

l a pl a ce t r an s f or m (e^{t} - e^{- t})^{2}

\int 512 x^{2} cos (8 x) d x

\frac{d}{d x} (ln (\frac{sin ( x )}{x}))

a re a y = 4 ln (x), y = x ln (x)