derivative of e^{x/(x-3})

解答

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

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

求解步骤

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

使用连锁律:

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

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

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

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

化简

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

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